Inventiones mathematicae最新文献

{"title":"The anisotropic Bernstein problem","authors":"Connor Mooney, Yang Yang","doi":"10.1007/s00222-023-01222-4","DOIUrl":"https://doi.org/10.1007/s00222-023-01222-4","url":null,"abstract":"Abstract We construct nonlinear entire anisotropic minimal graphs over $mathbb{R}^{4}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> , completing the solution to the anisotropic Bernstein problem. The examples we construct have a variety of growth rates, and our approach both generalizes to higher dimensions and recovers and elucidates known examples of nonlinear entire minimal graphs over $mathbb{R}^{n},, n geq 8$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>8</mml:mn> </mml:math> .","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135592232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Character levels and character bounds for finite classical groups","authors":"Robert M. Guralnick, Michael Larsen, Pham Huu Tiep","doi":"10.1007/s00222-023-01221-5","DOIUrl":"https://doi.org/10.1007/s00222-023-01221-5","url":null,"abstract":"Abstract The main results of the paper develop a level theory and establish strong character bounds for finite classical groups, in the case that the centralizer of the element has small order compared to $|G|$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>|</mml:mo> <mml:mi>G</mml:mi> <mml:mo>|</mml:mo> </mml:math> in a logarithmic sense.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135132129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonuniformly elliptic Schauder theory","authors":"Cristiana De Filippis, Giuseppe Mingione","doi":"10.1007/s00222-023-01216-2","DOIUrl":"https://doi.org/10.1007/s00222-023-01216-2","url":null,"abstract":"Abstract Local Schauder theory holds in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic problems are locally Hölder continuous if so are their coefficients.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135536574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-reductive geometric invariant theory and hyperbolicity","authors":"Gergely Bérczi, Frances Kirwan","doi":"10.1007/s00222-023-01219-z","DOIUrl":"https://doi.org/10.1007/s00222-023-01219-z","url":null,"abstract":"Abstract The Green–Griffiths–Lang and Kobayashi hyperbolicity conjectures for generic hypersurfaces of polynomial degree are proved using intersection theory for non-reductive geometric invariant theoretic quotients and recent work of Riedl and Yang.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134904364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the birational section conjecture with strong birationality assumptions","authors":"Giulio Bresciani","doi":"10.1007/s00222-023-01220-6","DOIUrl":"https://doi.org/10.1007/s00222-023-01220-6","url":null,"abstract":"Abstract Let $X$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> </mml:math> be a curve over a field $k$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>k</mml:mi> </mml:math> finitely generated over ℚ and $t$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>t</mml:mi> </mml:math> an indeterminate. We prove that, if $s$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>s</mml:mi> </mml:math> is a section of $pi _{1}(X)to operatorname{Gal}(k)$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>π</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> <mml:mo>→</mml:mo> <mml:mo>Gal</mml:mo> <mml:mo>(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>)</mml:mo> </mml:math> such that the base change $s_{k(t)}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msub> </mml:math> is birationally liftable, then $s$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>s</mml:mi> </mml:math> comes from geometry. As a consequence we prove that the section conjecture is equivalent to the cuspidalization of all sections over all finitely generated fields.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134904248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Moment maps and cohomology of non-reductive quotients","authors":"Gergely Bérczi, Frances Kirwan","doi":"10.1007/s00222-023-01218-0","DOIUrl":"https://doi.org/10.1007/s00222-023-01218-0","url":null,"abstract":"Abstract Let $H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>H</mml:mi> </mml:math> be a complex linear algebraic group with internally graded unipotent radical acting on a complex projective variety $X$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> </mml:math> . Given an ample linearisation of the action and an associated Fubini–Study Kähler form which is invariant for a maximal compact subgroup $Q$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Q</mml:mi> </mml:math> of $H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>H</mml:mi> </mml:math> , we define a notion of moment map for the action of $H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>H</mml:mi> </mml:math> , and under suitable conditions (that the linearisation is well-adapted and semistability coincides with stability) we describe the (non-reductive) GIT quotient $X/!/H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:mi>H</mml:mi> </mml:math> introduced in (Bérczi et al. in J. Topol. 11(3):826–855, 2018) in terms of this moment map. Using this description we derive formulas for the Betti numbers of $X/!/H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:mi>H</mml:mi> </mml:math> and express the rational cohomology ring of $X/!/H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:mi>H</mml:mi> </mml:math> in terms of the rational cohomology ring of the GIT quotient $X/!/T^{H}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mi>H</mml:mi> </mml:msup> </mml:math> , where $T^{H}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>T</mml:mi> <mml:mi>H</mml:mi> </mml:msup> </mml:math> is a maximal torus in $H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>H</mml:mi> </mml:math> . We relate intersection pairings on $X/!/H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:mi>H</mml:mi> </mml:math> to intersection pairings on $X/!/T^{H}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mi>H</mml:mi> </mml:msup> </mml:math> , obtaining a residue formula for these pairings on $X/!/H$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>X</mml:mi> <mml:mo>/</mml:mo> <mml:mo>/</mml:mo> <mml:mi>H</mml:mi> </mml:math> analogous to the residue formula of (Jeffrey and Kirwan in Topology 34(2):291–327, 1995). As an application, we announce a proof of the Green–Griffiths–Lang and Kobayashi conjectures for projective hypersurfaces with polynomial degree.","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134904363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Chabauty–Coleman bound for surfaces","authors":"Jerson Caro, Hector Pasten","doi":"10.1007/s00222-023-01217-1","DOIUrl":"https://doi.org/10.1007/s00222-023-01217-1","url":null,"abstract":"","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136263831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A proof of the Kudla–Rapoport conjecture for Krämer models","authors":"Qiao He, Chao Li, Yousheng Shi, Tonghai Yang","doi":"10.1007/s00222-023-01209-1","DOIUrl":"https://doi.org/10.1007/s00222-023-01209-1","url":null,"abstract":"","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"234 1","pages":"721 - 817"},"PeriodicalIF":3.1,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48574136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The maximal subgroups of the exceptional groups $F_{4}(q)$ , $E_{6}(q)$ and $^{2}!E_{6}(q)$ and related almost simple groups","authors":"David A. Craven","doi":"10.1007/s00222-023-01208-2","DOIUrl":"https://doi.org/10.1007/s00222-023-01208-2","url":null,"abstract":"<p>This article produces a complete list of all maximal subgroups of the finite simple groups of type <span>(F_{4})</span>, <span>(E_{6})</span> and twisted <span>(E_{6})</span> over all finite fields. Along the way, we determine the collection of Lie primitive almost simple subgroups of the corresponding algebraic groups. We give the stabilizers under the actions of outer automorphisms, from which one can obtain complete information about the maximal subgroups of all almost simple groups with socle one of these groups. We also provide a new maximal subgroup of <span>(^{2}!F_{4}(8))</span>, correcting the maximal subgroups for that group from the list of Malle. This provides the first new exceptional groups of Lie type to have their maximal subgroups enumerated for three decades. The techniques are a mixture of algebraic groups, representation theory, computational algebra, and use of the trilinear form on the 27-dimensional minimal module for <span>(E_{6})</span>. We provide a collection of supplementary Magma files that prove the author’s computational claims, yielding existence and the number of conjugacy classes of all maximal subgroups mentioned in the text.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"66 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gelfand–Kirillov dimension and mod pdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$p$end{document} cohomology for GL2","authors":"C. Breuil, F. Herzig, Yong Hu, Stefano Morra, Benjamin Schraen","doi":"10.1007/s00222-023-01202-8","DOIUrl":"https://doi.org/10.1007/s00222-023-01202-8","url":null,"abstract":"","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":"234 1","pages":"1 - 128"},"PeriodicalIF":3.1,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46183941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}