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0000b052-8d25-5cf2-80d0-1e797972013b | Characterization of integrable functions with almost-everywhere convergent Fourier series | Let \(\mathbb T=\mathbb R/\mathbb Z\), identified with \(I=[0,1)\) equipped with Lebesgue measure \(m\). For \(f\in L^1(\mathbb T)\), define
\[
\widehat f(k)=\int_I f(x)e^{-2\pi i kx}\,dx,\qquad
S_nf(x)=\sum_{|k|\le n}\widehat f(k)e^{2\pi i kx}.
\]
Characterize the set of all \(f\in L^1(\mathbb T)\) for which the seque... | open | null | null | null | null | 629f7824e411b8efdec59e292a5e6ee336766d8a5c6d88db8a0e0ae403b588e7 | problem-v1 | mathdb | https://ems.press/journals/owr/articles/12866 | {"schema_version": 1, "problem": {"id": "0000b052-8d25-5cf2-80d0-1e797972013b", "title": "Characterization of integrable functions with almost-everywhere convergent Fourier series", "statement": "Let \\(\\mathbb T=\\mathbb R/\\mathbb Z\\), identified with \\(I=[0,1)\\) equipped with Lebesgue measure \\(m\\). For \\(f\\... | 38,406 |
0000fc01-177e-5b5e-9ed6-3d6423d615e2 | The nilpotent-model irreducibility conjecture for Hamiltonian fibers | Let $G$ be a connected reductive group, let $H$ be a subgroup, let $\eta$ be a nilpotent element, and let $V$ be an $H$-variety. Write $X=M_G(H,\eta,V)$ for the associated Hamiltonian model variety. Property (Irr) means that every fiber of the quotient morphism
$$
\widetilde{\psi}_{G,X}/\!/G:X/\!/G\longrightarrow C_{G... | open | null | null | null | null | 39c20efeff48ac209b536a74cd29e0e2938f2e007883a2ce5fc2629810364f43 | problem-v1 | mathdb | https://arxiv.org/abs/math/0703296 | {"schema_version": 1, "problem": {"id": "0000fc01-177e-5b5e-9ed6-3d6423d615e2", "title": "The nilpotent-model irreducibility conjecture for Hamiltonian fibers", "statement": "Let $G$ be a connected reductive group, let $H$ be a subgroup, let $\\eta$ be a nilpotent element, and let $V$ be an $H$-variety. Write $X=M_G(H,... | 22,558 |
00022c2c-eee7-5fc5-922d-88b6e301f0a5 | Size of the adjacent zone in simultaneous space–time wavelet solutions | Determine the correct size of the adjacent zone, that is, the appropriate number of neighbouring points to retain for a simultaneous space–time solution. | open | null | null | null | null | 68d451338ba6cb1aa9b1977edd54c24ed0ed49f55ec16e7ce1f0223d51cf5647 | problem-v1 | mathdb | https://ems.press/journals/owr/articles/736 | {"schema_version": 1, "problem": {"id": "00022c2c-eee7-5fc5-922d-88b6e301f0a5", "title": "Size of the adjacent zone in simultaneous space–time wavelet solutions", "statement": "Determine the correct size of the adjacent zone, that is, the appropriate number of neighbouring points to retain for a simultaneous space–time... | 40,881 |
000283b5-4832-5762-b18f-81001bd4f747 | Delecroix–Lelièvre's orbit-count conjecture in \mathcal{H}(4) | Let $n$ be an integer greater than $8$, and consider primitive $n$-squared origamis in $\mathcal{H}(4)$, with $\mathcal{H}^{\mathrm{odd}}(4)$ denoting the odd component and $\mathcal{H}^{\mathrm{hyp}}(4)$ the hyperelliptic component. **Delecroix–Lelièvre's orbit-count conjecture.** The number of $\operatorname{SL}(2,\m... | open | null | null | null | null | 4575b1871b926af4137d83fdbc3b7b8a1167961bca30554fbec54104cdc81195 | problem-v1 | mathdb | https://arxiv.org/abs/2602.21984 | {"schema_version": 1, "problem": {"id": "000283b5-4832-5762-b18f-81001bd4f747", "title": "Delecroix–Lelièvre's orbit-count conjecture in \\mathcal{H}(4)", "statement": "Let $n$ be an integer greater than $8$, and consider primitive $n$-squared origamis in $\\mathcal{H}(4)$, with $\\mathcal{H}^{\\mathrm{odd}}(4)$ denoti... | 27,122 |
00028caf-2cd4-5fcc-a0c1-69b9b1a83965 | The local square-energy conjecture in logarithmic intervals | For a finite set $E$ of squares in the short interval
$$
E\subset\{k^2:N\le k\le N+N/(\log N)^\delta\},
$$
let $r_{E+E}(m)$ count representations of $m$ as a sum of two elements of $E$. **The local energy conjecture.** There exists $\delta>0$ such that
$$
\sum_m r_{E+E}^2(m)\ll |E|^2.
$$
The source introduces this ... | open | null | null | null | null | 3c083e10e252d391c444bbae0623aeb3379a6612389afb9440ff749956ffd363 | problem-v1 | mathdb | https://arxiv.org/abs/math/0608109 | {"schema_version": 1, "problem": {"id": "00028caf-2cd4-5fcc-a0c1-69b9b1a83965", "title": "The local square-energy conjecture in logarithmic intervals", "statement": "For a finite set $E$ of squares in the short interval\n\n$$\nE\\subset\\{k^2:N\\le k\\le N+N/(\\log N)^\\delta\\},\n$$\n\nlet $r_{E+E}(m)$ count represent... | 23,460 |
000307b1-3185-57c2-8698-48ea0d16c37e | Equivariant homotopy 3 — Figure out how to do equivariant stable homotopy theory without restriction on the group. | Figure out how to do equivariant stable homotopy theory without restriction on the group. Here you are going to have to change the current setup a lot, I think. Mike Mandell has some ideas about this. He points out that a lot of the crucial problems in mathematics concern infinite discrete groups, like the Novikov conj... | open | null | null | null | null | 1f2f01ce465adafa8c905469dc036f472965dfe5964d5b618e7afbdea2053e1f | problem-v1 | unsolvedmath | https://huggingface.co/datasets/ulamai/UnsolvedMath | {"schema_version": 1, "problem": {"id": "000307b1-3185-57c2-8698-48ea0d16c37e", "title": "Equivariant homotopy 3 — Figure out how to do equivariant stable homotopy theory without restriction on the group.", "statement": "Figure out how to do equivariant stable homotopy theory without restriction on the group. Here you ... | 12,090 |
00034ac5-512f-59bd-9e4d-433f1ac9a81b | Main open problems (problem 3) | Prove that, in two dimensions, $0<\chi<1/2$ and $1/2<\xi<1$. | open | null | null | null | null | 0db1490401e59845cc44978e0a8f595fccb3a80debc230fef5e05eb98cd6818e | problem-v1 | mathdb | http://aimpl.org/firstpercolation/1/#ed2f7227f2b11f99ac79c437091f9172 | {"schema_version": 1, "problem": {"id": "00034ac5-512f-59bd-9e4d-433f1ac9a81b", "title": "Main open problems (problem 3)", "statement": "Prove that, in two dimensions, $0<\\chi<1/2$ and $1/2<\\xi<1$.", "context": null, "status": "open", "field": ["math.PR"], "conjecturer": null, "year": null, "source_url": "http://aimp... | 5,255 |
0003a17c-2a68-5b56-a0c9-e43c20a0aff9 | Berman–Wang–Wargo conjecture on odd induced subgraphs | Let $G$ be a connected simple graph of order $n$, and let $f_o(G)$ denote the maximum order of an induced subgraph in which every vertex has odd degree.
**Berman–Wang–Wargo conjecture.** For any connected simple graph $G$ of order $n$,
$$
f_o(G)\geq 2\left\lfloor\frac{n}{4}\right\rfloor.
$$
The conjecture is a propo... | open | null | null | null | null | 5546a0f12b64e685a25825fc3e2333d555773f55172e41b8ae26b8f8766eba90 | problem-v1 | mathdb | https://arxiv.org/abs/2211.10895 | {"schema_version": 1, "problem": {"id": "0003a17c-2a68-5b56-a0c9-e43c20a0aff9", "title": "Berman–Wang–Wargo conjecture on odd induced subgraphs", "statement": "Let $G$ be a connected simple graph of order $n$, and let $f_o(G)$ denote the maximum order of an induced subgraph in which every vertex has odd degree.\n\n**Be... | 33,228 |
00046283-e739-5a3b-8055-036be0319a3b | Excision for periodic dual Hopf cyclic homology of comodule algebras | Let $B$ be a Hopf algebra with an invertible antipode and let $X$ be a stable anti-Yetter–Drinfeld module. Let
$$
0\longrightarrow J\longrightarrow A\longrightarrow A/J\longrightarrow 0
$$
be a sequence of $B$-comodule algebras such that both $J$ and $A$ are $B$-co-projective. **Excision conjecture.** One has a 6-ter... | open | null | null | null | null | 069806ef413d48d541ec83f53d1d11537e36426b759b04deb3a7506155f5de53 | problem-v1 | mathdb | https://arxiv.org/abs/math/0511026 | {"schema_version": 1, "problem": {"id": "00046283-e739-5a3b-8055-036be0319a3b", "title": "Excision for periodic dual Hopf cyclic homology of comodule algebras", "statement": "Let $B$ be a Hopf algebra with an invertible antipode and let $X$ be a stable anti-Yetter–Drinfeld module. Let\n\n$$\n0\\longrightarrow J\\longri... | 2,513 |
00046b55-224c-5a4e-8979-7768a9a44795 | Loop-space conjecture for the space of core metrics on spheres | For a smooth manifold $\operatorname{M}^n$, fix an embedded disk $\operatorname{D}^n\subseteq \operatorname{M}^n$. Let $\operatorname{\mathcal{R}^\text{Cores}}(\operatorname{M}^n)$ denote the space of core metrics on $\operatorname{M}^n$. In particular, combining core metrics on spheres gives a binary operation
$$
\mu... | open | null | null | null | null | a7fba6d2717e8316687c0ec34cb123078cad20e8ee5e44620ab36c6002f9c3fc | problem-v1 | mathdb | https://arxiv.org/abs/2009.06199 | {"schema_version": 1, "problem": {"id": "00046b55-224c-5a4e-8979-7768a9a44795", "title": "Loop-space conjecture for the space of core metrics on spheres", "statement": "For a smooth manifold $\\operatorname{M}^n$, fix an embedded disk $\\operatorname{D}^n\\subseteq \\operatorname{M}^n$. Let $\\operatorname{\\mathcal{R}... | 65,621 |
00047869-7408-564b-b6e5-446ef2ad2e01 | Colliot-Thélène's zero-cycle conjecture for geometrically rational varieties | Let $K$ be a number field and let $X$ be a smooth geometrically rational variety over $K$. Assume that
$$
\operatorname{Pic}(X\otimes \overline{K})\cong \mathbf Z.
$$
**Colliot-Thélène's zero-cycle conjecture.** The Hasse principle holds for zero-cycles on $X$: if
$$
X(A)^{\operatorname{Br}(X)}\ne\emptyset,
$$
then... | open | null | null | null | null | 1be461a80bd0609ca3fe930a1bbe22f63ce087f1c727242f67146145c9868a2d | problem-v1 | mathdb | https://arxiv.org/abs/0902.0482 | {"schema_version": 1, "problem": {"id": "00047869-7408-564b-b6e5-446ef2ad2e01", "title": "Colliot-Thélène's zero-cycle conjecture for geometrically rational varieties", "statement": "Let $K$ be a number field and let $X$ be a smooth geometrically rational variety over $K$. Assume that\n\n$$\n\\operatorname{Pic}(X\\otim... | 10,807 |
0004a6d6-4155-5e41-b915-8a7bb7aa5c71 | The interpretation conjecture for the action of profinite words on subsets | Let $M$ be the finite monoid under consideration, let $X$ be its generating alphabet, let $R$ be the relevant set on which $
Omega(X)$ acts, and let $P(M)$ denote the power set of $M$. For $
\tau\in\Omega(X)$, define its interpretation $
\tau\Lambda\in P(M)$ recursively by the interpretation map described in the surrou... | open | null | null | null | null | ab6f305b0bbaf7124dce41531d8400dc10618b7abc4bc34a6b04a0103b84f5ac | problem-v1 | mathdb | https://arxiv.org/abs/0812.3499 | {"schema_version": 1, "problem": {"id": "0004a6d6-4155-5e41-b915-8a7bb7aa5c71", "title": "The interpretation conjecture for the action of profinite words on subsets", "statement": "Let $M$ be the finite monoid under consideration, let $X$ be its generating alphabet, let $R$ be the relevant set on which $\nOmega(X)$ act... | 66,978 |
00065b37-225f-53d3-b7b0-1eec7a3caf97 | Nonsingular intertwining conjecture for maxima of translates functions | Let $n\in\mathbb{N}$, let $\nu_1,\ldots,\nu_n>0$, let $K$ be a strictly concave and strictly monotone kernel function, and let $J$ be an upper semicontinuous $n$-field function. For node systems $\mathbf{x},\mathbf{y}\in Y$, let $\mathbf{m}(\mathbf{x})\leq\mathbf{m}(\mathbf{y})$ mean coordinatewise inequality. **Nonsin... | open | null | null | null | null | 41fb2f80accfd02e888e28be86d88c79b45dbbc78da6ae0a36d658a833991840 | problem-v1 | mathdb | https://arxiv.org/abs/2210.06387 | {"schema_version": 1, "problem": {"id": "00065b37-225f-53d3-b7b0-1eec7a3caf97", "title": "Nonsingular intertwining conjecture for maxima of translates functions", "statement": "Let $n\\in\\mathbb{N}$, let $\\nu_1,\\ldots,\\nu_n>0$, let $K$ be a strictly concave and strictly monotone kernel function, and let $J$ be an u... | 25,797 |
0007025e-855b-5186-8fbd-f7e216bd0d1e | HHU ergodicity conjecture for conservative partially hyperbolic diffeomorphisms | Let $f: M^3\rightarrow M^3$ be a $C^r$ ($r > 1$) conservative partially hyperbolic diffeomorphism of a closed 3-manifold that fails to be ergodic. Here, $E^s$ and $E^u$ denote the stable and unstable bundles of the partially hyperbolic splitting, and a mapping torus is the manifold obtained from a self-diffeomorphism o... | open | null | null | null | null | 3c2084835ddf46555d4bef053b119dbe1dce7ec895f8500a1159a0173419a394 | problem-v1 | mathdb | https://arxiv.org/abs/2506.00405 | {"schema_version": 1, "problem": {"id": "0007025e-855b-5186-8fbd-f7e216bd0d1e", "title": "HHU ergodicity conjecture for conservative partially hyperbolic diffeomorphisms", "statement": "Let $f: M^3\\rightarrow M^3$ be a $C^r$ ($r > 1$) conservative partially hyperbolic diffeomorphism of a closed 3-manifold that fails t... | 23,494 |
00086c42-ea4d-5e21-b8b4-8ad1899e5be1 | Baker's Dozen — Self-dual curves and surfaces | Extend the known results on projectively self-dual polygons and curves to projectively self-dual polyhedra and to projectively self-dual polygons in multidimensional projective spaces. | open | null | null | null | null | 8f4bb499d490cc1b1e1606775c4c33c630e085abb139280b59b6838aa5426b92 | problem-v1 | mathdb | https://amj.math.stonybrook.edu/html-articles/Files-2015-2024/14-01/ | {"schema_version": 1, "problem": {"id": "00086c42-ea4d-5e21-b8b4-8ad1899e5be1", "title": "Baker's Dozen — Self-dual curves and surfaces", "statement": "Extend the known results on projectively self-dual polygons and curves to projectively self-dual polyhedra and to projectively self-dual polygons in multidimensional pr... | 55,941 |
00088f9a-8208-5592-9017-2d49c880bdc9 | The interchange-process comparison inequality | Let $k\geq 2$, let $\mathcal S_k$ be the symmetric group on $k$ letters, and let $g:\mathcal S_k\to\mathbb R$ be any function. For nonnegative numbers $\gamma_1,\ldots,\gamma_{k-1}$, with an empty sum interpreted as zero and $(ij)\in\mathcal S_k$ denoting the transposition of $i$ and $j$, **the interchange-process comp... | open | null | null | null | null | 0cc62944307a453748902b6d1944ddf61546804977ebf05909c3a00a01c07bc7 | problem-v1 | mathdb | https://arxiv.org/abs/0906.1716 | {"schema_version": 1, "problem": {"id": "00088f9a-8208-5592-9017-2d49c880bdc9", "title": "The interchange-process comparison inequality", "statement": "Let $k\\geq 2$, let $\\mathcal S_k$ be the symmetric group on $k$ letters, and let $g:\\mathcal S_k\\to\\mathbb R$ be any function. For nonnegative numbers $\\gamma_1,\... | 4,932 |
00089574-3352-5164-9404-f08397bc3782 | Is nonvanishing of the pushfor- ward ν∗ [Y, \partialY ] \in Hn (BΓ, BΓ′ ; Q) an obstruction for the interior int(Y ) = Y − \partialY of Y to admit a complete psc metric,… | Is nonvanishing of the pushfor- ward ν∗ [Y, \partialY ] \in Hn (BΓ, BΓ′ ; Q) an obstruction for the interior int(Y ) = Y − \partialY of Y to admit a complete psc metric, provided that (a) The homomorphism Γ′ \to Γ is injective, or (b) The metric has finite volume? A special case of the above question is when Y and \par... | open | null | null | null | null | b445d8758eb39e5d7fc7e33938b4eaa51f0e37966063757b953b0e1c0e0f09a0 | problem-v1 | unsolvedmath | https://doi.org/10.4171/owr/2024/28 | {"schema_version": 1, "problem": {"id": "00089574-3352-5164-9404-f08397bc3782", "title": "Is nonvanishing of the pushfor- ward ν∗ [Y, \\partialY ] \\in Hn (BΓ, BΓ′ ; Q) an obstruction for the interior int(Y ) = Y − \\partialY of Y to admit a complete psc metric,…", "statement": "Is nonvanishing of the pushfor- ward ν∗ ... | 70,378 |
00089e2c-b21e-5272-9691-dba5b26fb134 | Sparsity conjecture for sets satisfying the prime number theorem | For real $x$ and $t>1$, let $S_{\left\lfloor x/n^t\right\rfloor,x}$ denote the set considered in the paper, with the function defining $S_{f,x}$ taken to be non-piecewise. **Sparsity conjecture.** The family of sets $S_{\left\lfloor x/n^t\right\rfloor,x}$ are the sparsest sets that satisfy the prime number theorem. The... | open | null | null | null | null | f5f873ae1b9030f943d4b3c6b53e9c91e756a223aff837d7a93ffc8f01ad8c67 | problem-v1 | mathdb | https://arxiv.org/abs/2304.08736 | {"schema_version": 1, "problem": {"id": "00089e2c-b21e-5272-9691-dba5b26fb134", "title": "Sparsity conjecture for sets satisfying the prime number theorem", "statement": "For real $x$ and $t>1$, let $S_{\\left\\lfloor x/n^t\\right\\rfloor,x}$ denote the set considered in the paper, with the function defining $S_{f,x}$ ... | 95,873 |
000926a1-6f02-5b5c-866d-6155b2dbe2ef | The Drinfeld analogue of Ogg's rational cyclic-subgroup conjecture | Let $A=\mathbb{F}_q[T]$, let $F$ be its fraction field, and let $\phi$ be a rank-$2$ Drinfeld $A$-module over $F$. Define
$$
C=\begin{cases}3,&q\neq 3,\\4,&q=3.\end{cases}
$$
**Drinfeld cyclic-subgroup conjecture.** If $\mathfrak{p}$ is a prime of $A$ with $\deg\mathfrak{p}\geq C$, then there is no $F$-rational $A$-s... | open | null | null | null | null | ff20a369d3c307020ae3d8af52c882c69cdefd4def9461c56947298af5aa7e68 | problem-v1 | mathdb | https://arxiv.org/abs/2410.05502 | {"schema_version": 1, "problem": {"id": "000926a1-6f02-5b5c-866d-6155b2dbe2ef", "title": "The Drinfeld analogue of Ogg's rational cyclic-subgroup conjecture", "statement": "Let $A=\\mathbb{F}_q[T]$, let $F$ be its fraction field, and let $\\phi$ be a rank-$2$ Drinfeld $A$-module over $F$. Define\n\n$$\nC=\\begin{cases}... | 99,493 |
00096256-35d7-5a07-b1f9-ad1e738fa27b | The expected p-adic rank conjecture for simple Abelian varieties | Let $A$ be a simple Abelian variety over ${\mathbb{Q}}$ of dimension $g$, let $\Gamma$ be a subgroup of $A({\mathbb{Q}})$ of rank $\ell$ over $\mathbb{Z}$, and let $p$ be a prime number. Let
$$
\log:A({\mathbb{Q}}_p)\rightarrow T_A({\mathbb{Q}}_p)
$$
denote the canonical map from the $p$-adic Lie group $A({\mathbb{Q}... | open | null | null | null | null | 7534d60cf12d24470c26f5de5e8858c5ee75f13953d3f450a417007b32fd9e57 | problem-v1 | mathdb | https://arxiv.org/abs/1012.4823 | {"schema_version": 1, "problem": {"id": "00096256-35d7-5a07-b1f9-ad1e738fa27b", "title": "The expected p-adic rank conjecture for simple Abelian varieties", "statement": "Let $A$ be a simple Abelian variety over ${\\mathbb{Q}}$ of dimension $g$, let $\\Gamma$ be a subgroup of $A({\\mathbb{Q}})$ of rank $\\ell$ over $\\... | 45,759 |
0009a34a-79e8-5b89-b24d-084007920cd7 | Admissibility of finite-dimensional unitary corepresentations | Let $\mathbb{G}$ be a locally compact quantum group, and let $C_0(\mathbb{G})$ be its reduced $C^*$-algebra. A finite-dimensional unitary corepresentation of $C_0(\mathbb{G})$ is called **admissible** when its contragredient corepresentation is also bounded. **Admissibility conjecture.** For any $\mathbb{G}$, the finit... | open | null | null | null | null | 9f99cf8bee94bf66497756601be0038409a096215c0d13047efb543517554725 | problem-v1 | mathdb | https://arxiv.org/abs/1307.1412 | {"schema_version": 1, "problem": {"id": "0009a34a-79e8-5b89-b24d-084007920cd7", "title": "Admissibility of finite-dimensional unitary corepresentations", "statement": "Let $\\mathbb{G}$ be a locally compact quantum group, and let $C_0(\\mathbb{G})$ be its reduced $C^*$-algebra. A finite-dimensional unitary corepresenta... | 62,426 |
000ad8cc-6a7c-5e7d-8e89-db3514ebc646 | Sznitman's transience implies ballisticity conjecture for uniformly elliptic RWRE | Let $d\ge 2$, let $l\in\mathbb S^{d-1}$, and consider a random walk in a uniformly elliptic i.i.d. environment on $\mathbb Z^d$. The walk is **transient in direction** $l$ when
$$
P_0(A_l)=1,
$$
where
$$
A_l:=\left\{\lim_{n\to\infty}X_n\cdot l=\infty\right\}.
$$
It is **ballistic in direction** $l$ when
$$
P_0\tex... | open | null | null | null | null | 74863b77ed933ff2d93ceb5139496a5840b94edd0d596f4375db80f03d59403d | problem-v1 | mathdb | https://arxiv.org/abs/1212.4020 | {"schema_version": 1, "problem": {"id": "000ad8cc-6a7c-5e7d-8e89-db3514ebc646", "title": "Sznitman's transience implies ballisticity conjecture for uniformly elliptic RWRE", "statement": "Let $d\\ge 2$, let $l\\in\\mathbb S^{d-1}$, and consider a random walk in a uniformly elliptic i.i.d. environment on $\\mathbb Z^d$.... | 45,508 |
000ae371-3963-5a71-bc2f-8fbe196402c4 | Non-Kähler nef intersection conjecture | Let $X$ be a compact complex manifold, let $\mathcal{N}\subset H^{1,1}(X,\mathbb{R})$ be its cone of nef $(1,1)$-classes, let $[\alpha]\in\mathcal{N}$, and let $V\subset X$ be a closed irreducible analytic subvariety of dimension $k>0$. **Nef intersection conjecture.** One has
$$
\int_V\alpha^k\geqslant 0.
$$
This qu... | open | null | null | null | null | 56857d197d7723e33cfd6c1e35bb7e8803fc0bd7af44430bebef8823d004245b | problem-v1 | mathdb | https://arxiv.org/abs/2309.00580 | {"schema_version": 1, "problem": {"id": "000ae371-3963-5a71-bc2f-8fbe196402c4", "title": "Non-Kähler nef intersection conjecture", "statement": "Let $X$ be a compact complex manifold, let $\\mathcal{N}\\subset H^{1,1}(X,\\mathbb{R})$ be its cone of nef $(1,1)$-classes, let $[\\alpha]\\in\\mathcal{N}$, and let $V\\subse... | 33,709 |
000b73ab-322b-5424-bfa0-084cff91098d | Bachmann's double stuffle completeness conjecture for bi-brackets | Let bi-brackets be the $q$-multiple zeta values defined in the paper, equipped with their stuffle and dual stuffle products and the duality relation. **Bachmann's double stuffle conjecture.** The resulting double stuffle (that is, stuffle and dual stuffle) relations exhaust all the relations between the bi-brackets. Eq... | open | null | null | null | null | 294e7558227380f8067d46cae749a16d7754f397ebd093f3dc563ef3b44af387 | problem-v1 | mathdb | https://arxiv.org/abs/1412.0163 | {"schema_version": 1, "problem": {"id": "000b73ab-322b-5424-bfa0-084cff91098d", "title": "Bachmann's double stuffle completeness conjecture for bi-brackets", "statement": "Let bi-brackets be the $q$-multiple zeta values defined in the paper, equipped with their stuffle and dual stuffle products and the duality relation... | 15,965 |
000c48d5-c317-5334-9685-299ac7d7aac0 | Fukaya's Whitehead torsion conjecture for Floer complexes | Let $L_1$ and $L_2$ be exact Lagrangians with Floer homology $HF(L_1,L_2)$ and Floer complex $CF(L_1,L_2)$, whose Whitehead torsion is denoted by $\tau(CF(L_1,L_2))$. **Fukaya's conjecture.** If
$$
HF(L_1,L_2)=0
$$
and
$$
\tau(CF(L_1,L_2))=0,
$$
then there exists an exact symplectic diffeomorphism $\phi$ such that
... | open | null | null | null | null | 7f44696411797e4c898594136eee4c04cf795f060faca73e0a80df4fc17ed486 | problem-v1 | mathdb | https://arxiv.org/abs/1412.0697 | {"schema_version": 1, "problem": {"id": "000c48d5-c317-5334-9685-299ac7d7aac0", "title": "Fukaya's Whitehead torsion conjecture for Floer complexes", "statement": "Let $L_1$ and $L_2$ be exact Lagrangians with Floer homology $HF(L_1,L_2)$ and Floer complex $CF(L_1,L_2)$, whose Whitehead torsion is denoted by $\\tau(CF(... | 49,643 |
000c6e51-b4ad-59b1-aa7f-72381310e13b | Path $P_6$ edge-inducibility conjecture | Let $P_6$ be the path on six vertices. The paper establishes the bounds
$$
\frac{5}{372}\leq \operatorname{eind}(P_6)\leq \frac{1}{36}.
$$
**Path $P_6$ edge-inducibility conjecture.** The lower bound is exact:
$$
\operatorname{eind}(P_6)=\frac{5}{372}.
$$
The conjecture concerns one of the paper's remaining unsettl... | open | null | null | null | null | ed681544ccddd1a878c115fdfd60f061e63eb42ae6ebf9a9eac204154f3c58fb | problem-v1 | mathdb | https://arxiv.org/abs/2509.24064 | {"schema_version": 1, "problem": {"id": "000c6e51-b4ad-59b1-aa7f-72381310e13b", "title": "Path $P_6$ edge-inducibility conjecture", "statement": "Let $P_6$ be the path on six vertices. The paper establishes the bounds\n\n$$\n\\frac{5}{372}\\leq \\operatorname{eind}(P_6)\\leq \\frac{1}{36}.\n$$\n\n**Path $P_6$ edge-indu... | 92,611 |
000c8dae-d871-567f-9d36-c8d0f08ab3e0 | Give a concrete description of the probability measures that are the distributions of the self-adjoint bimonotone limit operators \lambda_t^*+\lambda_t+\rho_t^*+\rho_t. | Give a concrete description of the probability measures that are the distributions of the self-adjoint bimonotone limit operators \lambda_t^*+\lambda_t+\rho_t^*+\rho_t. | open | null | null | null | null | b2a108136af1a1bf913542fe44e25f0e5468c3805052c1848e476bff229f4d1f | problem-v1 | unsolvedmath | https://doi.org/10.4171/owr/2018/22 | {"schema_version": 1, "problem": {"id": "000c8dae-d871-567f-9d36-c8d0f08ab3e0", "title": "Give a concrete description of the probability measures that are the distributions of the self-adjoint bimonotone limit operators \\lambda_t^*+\\lambda_t+\\rho_t^*+\\rho_t.", "statement": "Give a concrete description of the probab... | 69,734 |
000ca17d-2cd2-5afe-9521-c5e1403c9288 | Orlov's conjecture on strong exceptional collections for toric DM stacks | Let $Y$ be a smooth projective toric DeligneMumford stack, and let $D^b(Y)$ denote its bounded derived category. A **strong exceptional collection** is an exceptional collection whose higher Ext-groups between all members vanish.
**Orlov's conjecture.** For any smooth projective toric DM stack $Y,$ the derived categor... | open | null | null | null | null | 2f48421fc41186351d2f6bca3721c97a578b99ab37012eec52b319ea7e315f73 | problem-v1 | mathdb | https://arxiv.org/abs/1010.3755 | {"schema_version": 1, "problem": {"id": "000ca17d-2cd2-5afe-9521-c5e1403c9288", "title": "Orlov's conjecture on strong exceptional collections for toric DM stacks", "statement": "Let $Y$ be a smooth projective toric DeligneMumford stack, and let $D^b(Y)$ denote its bounded derived category. A **strong exceptional colle... | 18,342 |
000d0f2b-4339-5687-8d5b-7d6f69a385ea | Baum–Connes conjecture for actions with finite dynamic asymptotic dimension | Let \name{\Gamma} be a finitely generated group acting on a compact space \name{X}. If the action has finite dynamic asymptotic dimension, then the Baum–Connes conjecture holds for \name{\Gamma} with coefficients in \name{C(X)}. | open | null | null | null | null | 8a3d1c8eb193c8ed2959f99591b4634fef2c0115da52c9b0872b98093465468d | problem-v1 | mathdb | https://ems.press/journals/owr/articles/14748 | {"schema_version": 1, "problem": {"id": "000d0f2b-4339-5687-8d5b-7d6f69a385ea", "title": "Baum–Connes conjecture for actions with finite dynamic asymptotic dimension", "statement": "Let \\name{\\Gamma} be a finitely generated group acting on a compact space \\name{X}. If the action has finite dynamic asymptotic dimensi... | 53,955 |
000e1794-087d-5779-a11b-a9abbeee8def | Ma–Zha–She's quotient-group conjecture for conflict-avoiding codes | Let $p$ be an odd prime, let $\mathbb{Z}_p^{\times}$ be the multiplicative group of nonzero residues modulo $p$, and let $\langle -1,2\rangle$ be the subgroup generated by $-1$ and $2$. Suppose
$$
[\mathbb{Z}_p^{\times}:\langle -1,2\rangle]\geq 3.
$$
The quotient $\mathbb{Z}_p^{\times}/\langle -1,2\rangle$ is cyclic.... | open | null | null | null | null | 87e437eb697346cf6e73d235dd4ff44be23fb5d775ac2c64213389542eeeff87 | problem-v1 | mathdb | https://arxiv.org/abs/2302.01487 | {"schema_version": 1, "problem": {"id": "000e1794-087d-5779-a11b-a9abbeee8def", "title": "Ma–Zha–She's quotient-group conjecture for conflict-avoiding codes", "statement": "Let $p$ be an odd prime, let $\\mathbb{Z}_p^{\\times}$ be the multiplicative group of nonzero residues modulo $p$, and let $\\langle -1,2\\rangle$ ... | 53,034 |
000e5729-3fbc-59b0-ae29-e0f10bb8be3a | Pick-function conjecture for normalized multiple Gamma functions | Let $G_n$ be the multiple Gamma functions of order $n$, defined by $G_1(z)=\Gamma(z)$ and the recurrence
$$
G_{n+1}(z+1)=G_{n+1}(z)G_n(z),\qquad G_n(1)=1,
$$
for $z\in\mathbb{C}$ and $n\in\mathbb{N}$. For $z\in\mathbb{C}\setminus(-\infty,0]$, define
$$
f_n(z)=\frac{\log G_n(z+1)}{z^n\operatorname{Log}z}.
$$
**Pick-... | open | null | null | null | null | fb7a2513e03d063ba47a96bf5f7145245d019dd9975ca0e2737397231d7eade3 | problem-v1 | mathdb | https://arxiv.org/abs/1601.03167 | {"schema_version": 1, "problem": {"id": "000e5729-3fbc-59b0-ae29-e0f10bb8be3a", "title": "Pick-function conjecture for normalized multiple Gamma functions", "statement": "Let $G_n$ be the multiple Gamma functions of order $n$, defined by $G_1(z)=\\Gamma(z)$ and the recurrence\n\n$$\nG_{n+1}(z+1)=G_{n+1}(z)G_n(z),\\qqua... | 98,023 |
000edd4b-471f-5029-9fa1-15d6e1a5b26a | Finite endomorphic presentation conjecture for Fibonacci Lie algebras | Let $p=2$, let $\mathcal L=\operatorname{Lie}(v_1,v_2)$ be the Fibonacci Lie algebra, and let $\mathbf L=\operatorname{Lie}_p(v_1,v_2)$ be its Fibonacci restricted version. The source proposes that both algebras satisfy the listed defining relations and all their shifts under the shift endomorphism. **Finite endomorphi... | open | null | null | null | null | 14af65374c3e83d5f8fdd90c0b1b13d62e1ba0cda25d74d9e7a035e15a97d046 | problem-v1 | mathdb | https://arxiv.org/abs/2410.08832 | {"schema_version": 1, "problem": {"id": "000edd4b-471f-5029-9fa1-15d6e1a5b26a", "title": "Finite endomorphic presentation conjecture for Fibonacci Lie algebras", "statement": "Let $p=2$, let $\\mathcal L=\\operatorname{Lie}(v_1,v_2)$ be the Fibonacci Lie algebra, and let $\\mathbf L=\\operatorname{Lie}_p(v_1,v_2)$ be i... | 8,047 |
000efccf-a3db-5075-87b4-43b5df007a21 | Goldberg–Seymour conjecture for equality in Vizing’s multigraph bound | Let $G$ be a multigraph with maximum edge multiplicity $\\mu(G)\ge 2$. Then
\[
\chi'(G)=\Delta(G)+\mu(G)
\]
if and only if there exists an odd subset $S\subseteq V(G)$ with $|S|\ge 3$ such that
\[
|E[S]|>\frac{|S|-1}{2}\bigl(\Delta(G)+\mu(G)-1\bigr).
\] | open | null | null | null | null | 47f0fc5fa259730ad4bb83891fdc07e9b6bc379ad65f5ba4e0474b707410f1a4 | problem-v1 | mathdb | https://ems.press/journals/owr/articles/4212 | {"schema_version": 1, "problem": {"id": "000efccf-a3db-5075-87b4-43b5df007a21", "title": "Goldberg–Seymour conjecture for equality in Vizing’s multigraph bound", "statement": "Let $G$ be a multigraph with maximum edge multiplicity $\\\\mu(G)\\ge 2$. Then\n\\[\n\\chi'(G)=\\Delta(G)+\\mu(G)\n\\]\nif and only if there exi... | 28,101 |
00107f4d-38fe-548e-b113-aceebf63ca5d | Characterization conjecture for finite abelian groups by sets of lengths | Let $G$ be a finite abelian group, and let $\mathsf D(G)$ denote its Davenport constant. Let $\mathcal L(G)$ denote the system of sets of lengths associated with $G$. For an abelian group $G'$, assume that
$$
\mathcal L(G)=\mathcal L(G').
$$
**Characterization conjecture.** If $\mathsf D(G)\geq 4$, then $G$ and $G'$ ... | open | null | null | null | null | b572f288aeabdcc65f10bddafdf0f5599fd455625bd273678019591722d35d08 | problem-v1 | mathdb | https://arxiv.org/abs/1509.07462 | {"schema_version": 1, "problem": {"id": "00107f4d-38fe-548e-b113-aceebf63ca5d", "title": "Characterization conjecture for finite abelian groups by sets of lengths", "statement": "Let $G$ be a finite abelian group, and let $\\mathsf D(G)$ denote its Davenport constant. Let $\\mathcal L(G)$ denote the system of sets of l... | 70,835 |
00108a24-8636-5afc-bc6e-8feb0a0c9cee | Harary's Edge Reconstruction Conjecture for graphs | Let $G$ be a graph. An **edge-deck** is the multiset
$$
\mathcal{E}\mathcal{D}(G)=\\{G-e:e\in E(G)\\}.
$$
A graph is **edge-reconstructible** if it is uniquely determined, up to isomorphism, by its edge-deck. **Harary's Edge Reconstruction Conjecture.** Every graph with at least $4$ edges is edge-reconstructible, i.e... | open | null | null | null | null | 6f70302df874d0ec73df270b7edf9c59bd397bd4f2bf6af00e674fed50ce4c98 | problem-v1 | mathdb | https://arxiv.org/abs/2210.00338 | {"schema_version": 1, "problem": {"id": "00108a24-8636-5afc-bc6e-8feb0a0c9cee", "title": "Harary's Edge Reconstruction Conjecture for graphs", "statement": "Let $G$ be a graph. An **edge-deck** is the multiset\n\n$$\n\\mathcal{E}\\mathcal{D}(G)=\\\\{G-e:e\\in E(G)\\\\}.\n$$\n\nA graph is **edge-reconstructible** if it ... | 43,526 |
00109508-6f10-5507-bafb-f743581136e9 | Rationality of a generic cubic fourfold | Determine whether a generic cubic fourfold $X\subset \mathbb P^5_{\mathbb C}$ is rational. The report states that a generic member of this 20-dimensional family is expected to be non-rational. | open | null | null | null | null | 460aa1fca66d0981d85777119b84bcad0877eacfd71ada7ddfddfa1842f9770f | problem-v1 | mathdb | https://ems.press/journals/owr/articles/14611 | {"schema_version": 1, "problem": {"id": "00109508-6f10-5507-bafb-f743581136e9", "title": "Rationality of a generic cubic fourfold", "statement": "Determine whether a generic cubic fourfold $X\\subset \\mathbb P^5_{\\mathbb C}$ is rational. The report states that a generic member of this 20-dimensional family is expecte... | 27,322 |
0010cf37-c7d8-5170-9fac-705d9be059db | Euclidean distance degree for symmetric diagonal-zero rank-two varieties | Let $\mathcal{L}_2^S\subset\operatorname{Sym}_n(\mathbb{C})$ be the variety of symmetric matrices of rank at most $2$ with diagonal zero pattern $S=\{(1,1),\ldots,(s,s)\}$, where $s\in[4]$. **Symmetric diagonal-zero ED-degree conjecture.**
$$
\operatorname{EDdegree}(\mathcal{L}_2^S)=
\begin{cases}
3(n-1)-2 & \text{if ... | open | null | null | null | null | 3b66e6ee00c588b965afee7c71521800c797cd80418c900fc665b32c8da04fd1 | problem-v1 | mathdb | https://arxiv.org/abs/2010.15636 | {"schema_version": 1, "problem": {"id": "0010cf37-c7d8-5170-9fac-705d9be059db", "title": "Euclidean distance degree for symmetric diagonal-zero rank-two varieties", "statement": "Let $\\mathcal{L}_2^S\\subset\\operatorname{Sym}_n(\\mathbb{C})$ be the variety of symmetric matrices of rank at most $2$ with diagonal zero ... | 23,194 |
00116ef1-d03c-5612-a818-3938fe9f3276 | Existence conjecture for doubly saturated Ramsey-good graphs | Let $s,t \ge 3$ with $s \le t$ and $(s,t) \notin \{(3,4),(3,6)\}$. A graph is **doubly saturated $R(s,t)$-good** if it is $R(s,t)$-good and remains so under the relevant double-saturation condition described in the paper. **Existence conjecture.** For every such pair $(s,t)$, there is a doubly saturated $R(s,t)$-good g... | open | null | null | null | null | a3be48501d0f910e7251019128c1659f4f1411ecb1b7c75048d448541596075d | problem-v1 | mathdb | https://arxiv.org/abs/2604.21187 | {"schema_version": 1, "problem": {"id": "00116ef1-d03c-5612-a818-3938fe9f3276", "title": "Existence conjecture for doubly saturated Ramsey-good graphs", "statement": "Let $s,t \\ge 3$ with $s \\le t$ and $(s,t) \\notin \\{(3,4),(3,6)\\}$. A graph is **doubly saturated $R(s,t)$-good** if it is $R(s,t)$-good and remains ... | 64,017 |
0011a6cf-ff08-57a3-85fa-ba2ac62bbbce | Ratio of differences of fourth powers conjecture | A number $t$ is represented as a ratio of two differences of fourth powers if there exist integers or rational numbers $a,b,c,d$ such that
$$
t=\frac{a^4-b^4}{c^4-d^4},
$$
with $c^4-d^4\neq 0$. **Ratio of differences of fourth powers conjecture.** Every number can be written as the ratio of two differences of fourth ... | open | null | null | null | null | 87e1004062d1a9d20c2d84b32a9bced3611f63478db12c6517ebbb36efe12cd2 | problem-v1 | mathdb | https://arxiv.org/abs/1009.4306 | {"schema_version": 1, "problem": {"id": "0011a6cf-ff08-57a3-85fa-ba2ac62bbbce", "title": "Ratio of differences of fourth powers conjecture", "statement": "A number $t$ is represented as a ratio of two differences of fourth powers if there exist integers or rational numbers $a,b,c,d$ such that\n\n$$\nt=\\frac{a^4-b^4}{c... | 53,029 |
00129622-53c4-5c56-8579-e9fdcee6bedb | The stronger twisted coalgebra conjecture in right $mathbb{E}_d$-modules | Let $M$ be a simply connected parallelizable manifold of finite type and dimension $d$. Let $\operatorname{ch}(\mathsf{FM}_M)$, $M^+$, $\mathcal{I}$, $\operatorname{Tw}$, and $\operatorname{B}_\iota$ be as above, and let $\mathbb{E}_d$ be a model of the little-$d$-disks operad. The source gives a zig-zag of quasi-isomo... | open | null | null | null | null | 265e21905c8dafa6301fde0eb26d3c1b144d239fb40fdbbfb14e06a9360eb460 | problem-v1 | mathdb | https://arxiv.org/abs/2606.26802 | {"schema_version": 1, "problem": {"id": "00129622-53c4-5c56-8579-e9fdcee6bedb", "title": "The stronger twisted coalgebra conjecture in right $mathbb{E}_d$-modules", "statement": "Let $M$ be a simply connected parallelizable manifold of finite type and dimension $d$. Let $\\operatorname{ch}(\\mathsf{FM}_M)$, $M^+$, $\\m... | 14,850 |
0012a10c-3bc1-514f-8efc-6593ef88dfeb | Effective certificates and the witness gap for rationality and unirationality | Let $X$ be a variety over $\overline{\mathbb Q}$. Is there an algorithm to determine whether
$X$ is rational?
Same question for unirationality. | open | null | null | null | null | 2c16de0b8899ab3ed9a04c5e4a63edd3777c3b04d86d4a84edd30061121b5fe3 | problem-v1 | unsolvedmath | http://aimpl.org/rationalityag/1/ | {"schema_version": 1, "problem": {"id": "0012a10c-3bc1-514f-8efc-6593ef88dfeb", "title": "Effective certificates and the witness gap for rationality and unirationality", "statement": "Let $X$ be a variety over $\\overline{\\mathbb Q}$. Is there an algorithm to determine whether\n$X$ is rational?\n\nSame question for un... | 17,101 |
001405d1-4d7f-51d8-9647-72ead9441aea | The relative Hitchin metric gluing conjecture | Let $S$ be a smooth complex curve, let $X\to S$ be a polarized smooth family of smooth projective curves of genus at least $2$, and let $g:M^{s}_{Hig}(X/S,r)\to S$ be the relative moduli space of rank-$r$ stable Higgs bundles of degree zero, equipped with its relative Higgs field $\theta_{KS}$. For each fiber $Y_s$, le... | open | null | null | null | null | 3dc0c54c16a85a68bcb1b067764d5d38a9fdda4eeb78d367da71966152a15e37 | problem-v1 | mathdb | https://arxiv.org/abs/2512.04809 | {"schema_version": 1, "problem": {"id": "001405d1-4d7f-51d8-9647-72ead9441aea", "title": "The relative Hitchin metric gluing conjecture", "statement": "Let $S$ be a smooth complex curve, let $X\\to S$ be a polarized smooth family of smooth projective curves of genus at least $2$, and let $g:M^{s}_{Hig}(X/S,r)\\to S$ be... | 24,124 |
001433e4-afa6-59e6-bb12-8b1b4fc06f7c | Numerical versus rational triviality for polynomials in symmetric divisor classes | Let $A$ be an abelian variety. If $P\in \operatorname{CH}^*(A)$ is a polynomial with rational coefficients in the first Chern classes of symmetric line bundles on $A$, then $P$ is numerically equivalent to zero if and only if $P$ is rationally equivalent to zero. | open | null | null | null | null | c9b1992ac5265656a654a6267f6b7fd10477c48a7c5b09551ecdc7f2339debac | problem-v1 | mathdb | https://ems.press/journals/owr/articles/13101 | {"schema_version": 1, "problem": {"id": "001433e4-afa6-59e6-bb12-8b1b4fc06f7c", "title": "Numerical versus rational triviality for polynomials in symmetric divisor classes", "statement": "Let $A$ be an abelian variety. If $P\\in \\operatorname{CH}^*(A)$ is a polynomial with rational coefficients in the first Chern clas... | 78,682 |
00151550-79c0-52ed-ba67-9321c7948c95 | Bøgvad's conjecture for smooth polytopes | Let $P$ be a smooth lattice polytope, and let $I_P$ denote its toric ideal.
**Bøgvad's conjecture.** The toric ideal $I_P$ is quadratic.
This is presented as one of the important conjectures on toric ideals. The source does not provide a resolution or further status evidence here. | open | null | null | null | null | 5610e3bdf8e2e293c0a0c6f8a0d9f8a6ec423bfef708df1597b665132dab5658 | problem-v1 | mathdb | https://arxiv.org/abs/2606.20430 | {"schema_version": 1, "problem": {"id": "00151550-79c0-52ed-ba67-9321c7948c95", "title": "Bøgvad's conjecture for smooth polytopes", "statement": "Let $P$ be a smooth lattice polytope, and let $I_P$ denote its toric ideal.\n\n**Bøgvad's conjecture.** The toric ideal $I_P$ is quadratic.\n\nThis is presented as one of th... | 33,516 |
0015c2c5-a8f9-5bd3-b000-d177892a479d | Uniform boundedness conjecture for ranks of quadratic twists | Let $E$ be an elliptic curve over a number field $k$, and call an elliptic curve $E'$ over $k$ a **quadratic twist** of $E$ when it is obtained from $E$ by a quadratic twisting operation over $k$.
**Uniform boundedness conjecture for ranks of quadratic twists.** There is a positive integer $R=R(E,k)$ such that every e... | open | null | null | null | null | d807a40e9bbc1edd978eee458d30ca97d44caf172b46460742363e1e795ce63e | problem-v1 | mathdb | https://arxiv.org/abs/1805.11205 | {"schema_version": 1, "problem": {"id": "0015c2c5-a8f9-5bd3-b000-d177892a479d", "title": "Uniform boundedness conjecture for ranks of quadratic twists", "statement": "Let $E$ be an elliptic curve over a number field $k$, and call an elliptic curve $E'$ over $k$ a **quadratic twist** of $E$ when it is obtained from $E$ ... | 84,251 |
0016852b-70e1-525e-b5f2-3d950bd7a6cc | The figurate-prime Goldbach conjecture | A **figurate prime** is a number of the form $\binom{p^a}{i}$, where $p$ is prime and $a,i\in\mathbb{Z}^+$. **The figurate-prime Goldbach conjecture.** Every positive integer $n>1$ can be expressed as the sum of two figurate primes. Computations verify the claim for $1<n\leq10^7$, but the general assertion remains open... | open | null | null | null | null | 02609f6afa8f5dab41c6f7dd3bdf9976681798ba57d4ed9e1e2fdf44b961e9ec | problem-v1 | mathdb | https://arxiv.org/abs/1406.5661 | {"schema_version": 1, "problem": {"id": "0016852b-70e1-525e-b5f2-3d950bd7a6cc", "title": "The figurate-prime Goldbach conjecture", "statement": "A **figurate prime** is a number of the form $\\binom{p^a}{i}$, where $p$ is prime and $a,i\\in\\mathbb{Z}^+$. **The figurate-prime Goldbach conjecture.** Every positive integ... | 881 |
00171a8f-cc75-5c71-add0-254448166564 | Eventual linearity of projective dimension and regularity for symmetric-invariant ideal chains | Let $K$ be a field and let $c\ge 1$. For $n\ge 1$, set $R_n=K[X_{c\times n}]=K[X_{i,j}:1\le i\le c,\ 1\le j\le n]$, with the action of $\operatorname{Sym}(n)$ given by $\sigma\cdot X_{k,j}=X_{k,\sigma(j)}$. Let $(I_n)_{n\ge 1}$ be a $\operatorname{Sym}$-invariant chain of ideals, meaning that $I_n\subseteq R_n$ is $\op... | open | null | null | null | null | f03d03fb29fdf69f2e95556a19d1d2343a5fc9cf0f7cde0f31d3d1bff62013e3 | problem-v1 | mathdb | https://ems.press/journals/owr/articles/2654827 | {"schema_version": 1, "problem": {"id": "00171a8f-cc75-5c71-add0-254448166564", "title": "Eventual linearity of projective dimension and regularity for symmetric-invariant ideal chains", "statement": "Let $K$ be a field and let $c\\ge 1$. For $n\\ge 1$, set $R_n=K[X_{c\\times n}]=K[X_{i,j}:1\\le i\\le c,\\ 1\\le j\\le ... | 93,694 |
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