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$hat{G}$-local systems on smooth projective curves are potentially automorphic 光滑投影曲线上的$hat{G}$-局部系统是潜在自同构的
IF 3.7 1区 数学
Acta Mathematica Pub Date : 2016-09-12 DOI: 10.4310/acta.2019.v223.n1.a1
Gebhard Bockle, M. Harris, Chandrashekhar B. Khare, J. Thorne
{"title":"$hat{G}$-local systems on smooth projective curves are potentially automorphic","authors":"Gebhard Bockle, M. Harris, Chandrashekhar B. Khare, J. Thorne","doi":"10.4310/acta.2019.v223.n1.a1","DOIUrl":"https://doi.org/10.4310/acta.2019.v223.n1.a1","url":null,"abstract":"Let $X$ be a smooth, projective, geometrically connected curve over a finite field $mathbb{F}_q$, and let $G$ be a split semisimple algebraic group over $mathbb{F}_q$. Its dual group $widehat{G}$ is a split reductive group over $mathbb{Z}$. Conjecturally, any $l$-adic $widehat{G}$-local system on $X$ (equivalently, any conjugacy class of continuous homomorphisms $pi_1(X) to widehat{G}(overline{mathbb{Q}}_l)$) should be associated to an everywhere unramified automorphic representation of the group $G$. \u0000We show that for any homomorphism $pi_1(X) to widehat{G}(overline{mathbb{Q}}_l)$ of Zariski dense image, there exists a finite Galois cover $Y to X$ over which the associated local system becomes automorphic.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"1 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2016-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71152943","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}
引用次数: 40
Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders 任意自由度和通常双曲不变圆柱体中的阿诺德扩散
IF 3.7 1区 数学
Acta Mathematica Pub Date : 2016-09-01 DOI: 10.1007/s11511-016-0141-5
P. Bernard, V. Kaloshin, Ke Zhang
{"title":"Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders","authors":"P. Bernard, V. Kaloshin, Ke Zhang","doi":"10.1007/s11511-016-0141-5","DOIUrl":"https://doi.org/10.1007/s11511-016-0141-5","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"217 1","pages":"1-79"},"PeriodicalIF":3.7,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11511-016-0141-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53064704","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}
引用次数: 37
Sur la répresentation analytique d'une branche uniforme d'une fonction monogène 一元函数的统一分支的解析表示
IF 3.7 1区 数学
Acta Mathematica Pub Date : 2016-06-11 DOI: 10.1007/BF02404411
G. Mittag-Leffler
{"title":"Sur la répresentation analytique d'une branche uniforme d'une fonction monogène","authors":"G. Mittag-Leffler","doi":"10.1007/BF02404411","DOIUrl":"https://doi.org/10.1007/BF02404411","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"34 1","pages":"285-308"},"PeriodicalIF":3.7,"publicationDate":"2016-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/BF02404411","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52296821","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}
引用次数: 114
Bounds on the topology and index of minimal surfaces 拓扑的边界和最小曲面的索引
IF 3.7 1区 数学
Acta Mathematica Pub Date : 2016-05-09 DOI: 10.4310/acta.2019.v223.n1.a2
W. Meeks, Joaquín Pérez, A. Ros
{"title":"Bounds on the topology and index of minimal surfaces","authors":"W. Meeks, Joaquín Pérez, A. Ros","doi":"10.4310/acta.2019.v223.n1.a2","DOIUrl":"https://doi.org/10.4310/acta.2019.v223.n1.a2","url":null,"abstract":"We prove that for every nonnegative integer $g$, there exists a bound on the number of ends of a complete, embedded minimal surface $M$ in $mathbb{R}^3$ of genus $g$ and finite topology. This bound on the finite number of ends when $M$ has at least two ends implies that $M$ has finite stability index which is bounded by a constant that only depends on its genus.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"1 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2016-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71152957","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}
引用次数: 7
On Thurston’s Euler class-one conjecture 关于瑟斯顿的欧拉一类猜想
IF 3.7 1区 数学
Acta Mathematica Pub Date : 2016-03-11 DOI: 10.4310/ACTA.2020.V225.N2.A3
David Gabai, Mehdi Yazdi
{"title":"On Thurston’s Euler class-one conjecture","authors":"David Gabai, Mehdi Yazdi","doi":"10.4310/ACTA.2020.V225.N2.A3","DOIUrl":"https://doi.org/10.4310/ACTA.2020.V225.N2.A3","url":null,"abstract":"In 1976, Thurston proved that taut foliations on closed hyperbolic 3-manifolds have Euler class of norm at most one, and conjectured that, conversely, any Euler class with norm equal to one is Euler class of a taut foliation. We construct counterexamples to this conjecture and suggest an alternative conjecture.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"1 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2016-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71153048","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}
引用次数: 5
The linear stability of the Schwarzschild solution to gravitational perturbations 史瓦西解对引力扰动的线性稳定性
IF 3.7 1区 数学
Acta Mathematica Pub Date : 2016-01-25 DOI: 10.4310/ACTA.2019.v222.n1.a1
Mihalis Dafermos, G. Holzegel, I. Rodnianski
{"title":"The linear stability of the Schwarzschild solution to gravitational perturbations","authors":"Mihalis Dafermos, G. Holzegel, I. Rodnianski","doi":"10.4310/ACTA.2019.v222.n1.a1","DOIUrl":"https://doi.org/10.4310/ACTA.2019.v222.n1.a1","url":null,"abstract":"We prove in this paper the linear stability of the celebrated Schwarzschild family of black holes in general relativity: Solutions to the linearisation of the Einstein vacuum equations around a Schwarzschild metric arising from regular initial data remain globally bounded on the black hole exterior and in fact decay to a linearised Kerr metric. We express the equations in a suitable double null gauge. To obtain decay, one must in fact add a residual pure gauge solution which we prove to be itself quantitatively controlled from initial data. Our result a fortiori includes decay statements for general solutions of the Teukolsky equation (satisfied by gauge-invariant null-decomposed curvature components). These latter statements are in fact deduced in the course of the proof by exploiting associated quantities shown to satisfy the Regge--Wheeler equation, for which appropriate decay can be obtained easily by adapting previous work on the linear scalar wave equation. The bounds on the rate of decay to linearised Kerr are inverse polynomial, suggesting that dispersion is sufficient to control the non-linearities of the Einstein equations in a potential future proof of nonlinear stability. This paper is self-contained and includes a physical-space derivation of the equations of linearised gravity around Schwarzschild from the full non-linear Einstein vacuum equations expressed in a double null gauge.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"1 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2016-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71153002","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}
引用次数: 153
Global theory of one-frequency Schrödinger operators 一频Schrödinger算子的全局理论
IF 3.7 1区 数学
Acta Mathematica Pub Date : 2015-10-20 DOI: 10.1007/S11511-015-0128-7
A. Avila
{"title":"Global theory of one-frequency Schrödinger operators","authors":"A. Avila","doi":"10.1007/S11511-015-0128-7","DOIUrl":"https://doi.org/10.1007/S11511-015-0128-7","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"215 1","pages":"1-54"},"PeriodicalIF":3.7,"publicationDate":"2015-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S11511-015-0128-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53064153","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}
引用次数: 183
Constructing entire functions by quasiconformal folding 拟共形折叠构造整个函数
IF 3.7 1区 数学
Acta Mathematica Pub Date : 2015-02-28 DOI: 10.1007/S11511-015-0122-0
C. Bishop
{"title":"Constructing entire functions by quasiconformal folding","authors":"C. Bishop","doi":"10.1007/S11511-015-0122-0","DOIUrl":"https://doi.org/10.1007/S11511-015-0122-0","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"214 1","pages":"1-60"},"PeriodicalIF":3.7,"publicationDate":"2015-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S11511-015-0122-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53063870","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}
引用次数: 93
Local Hodge theory of Soergel bimodules Soergel双模的局部Hodge理论
IF 3.7 1区 数学
Acta Mathematica Pub Date : 2014-10-08 DOI: 10.1007/s11511-017-0146-8
G. Williamson
{"title":"Local Hodge theory of Soergel bimodules","authors":"G. Williamson","doi":"10.1007/s11511-017-0146-8","DOIUrl":"https://doi.org/10.1007/s11511-017-0146-8","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"217 1","pages":"341-404"},"PeriodicalIF":3.7,"publicationDate":"2014-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11511-017-0146-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53064769","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}
引用次数: 14
HITCHIN CHARACTERS AND GEODESIC LAMINATIONS Hitchin字符和测地线分层
IF 3.7 1区 数学
Acta Mathematica Pub Date : 2014-10-02 DOI: 10.4310/ACTA.2017.v218.n2.a1
F. Bonahon, G. Dreyer
{"title":"HITCHIN CHARACTERS AND GEODESIC LAMINATIONS","authors":"F. Bonahon, G. Dreyer","doi":"10.4310/ACTA.2017.v218.n2.a1","DOIUrl":"https://doi.org/10.4310/ACTA.2017.v218.n2.a1","url":null,"abstract":"For a closed surface S, the Hitchin component Hitn(S) is a preferred component of the character variety consisting of group homomorphisms from the fundamental group �1(S) to the Lie group PSLn(R). We construct a parametrization of the Hitchin component that is well-adapted to a geodesic laminationon the surface. This is a natural extension of Thurston's parametrization of the Teichmuller space T(S) by shear coordinates associated to �, corresponding to the case n = 2. However, significantly new ideas are needed in this higher dimensional case. The article concludes with a few applications.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"218 1","pages":"201-295"},"PeriodicalIF":3.7,"publicationDate":"2014-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71152805","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}
引用次数: 22
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