Symmetric power functoriality for holomorphic modular forms, II

被引：79

作者：

Newton, James ^{[1
,2
]}

Thorne, Jack A. ^{[3
]}

机构：

[1] Kings Coll London, Dept Math, London WC2R 2LS, England

[2] Math Inst, Woodstock Rd, Oxford OX2 6GG, England

[3] Dept Pure Math & Math Stat, Wilberforce Rd, Cambridge CB3 0WB, England

来源：

PUBLICATIONS MATHEMATIQUES DE L IHES | 2021年 / 134卷 / 01期

基金：

欧洲研究理事会;

关键词：

GALOIS REPRESENTATIONS; CONJECTURE; AUTOMORPHY;

D O I：

10.1007/s10240-021-00126-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f be a cuspidal Hecke eigenform without complex multiplication. We prove the automorphy of the symmetric power lifting Symn f for every n >= 1.

引用

页码：117 / 152

页数：36

共 34 条

[21]

Gelbart S., 1975, Automorphic Forms on Adele Groups, Vno. 83

[22] Modularity lifting theorems for ordinary Galois representations [J].

Geraghty, David .

MATHEMATISCHE ANNALEN, 2019, 373 (3-4) :1341-1427

[23] Serre's modularity conjecture: The level one case [J].

Khare, Chandrashekhar .

DUKE MATHEMATICAL JOURNAL, 2006, 134 (03) :557-589

[24] Serre's modularity conjecture (I) [J].

Khare, Chandrashekhar ;

Wintenberger, Jean-Pierre .

INVENTIONES MATHEMATICAE, 2009, 178 (03) :485-504

[25] An example of non-normal quintic automorphic induction and modularity of symmetric powers of cusp forms of icosahedral type [J].

Kim, HH .

INVENTIONES MATHEMATICAE, 2004, 156 (03) :495-502

[26] Moduli of finite flat group schemes, and modularity [J].

Kisin, Mark .

ANNALS OF MATHEMATICS, 2009, 170 (03) :1085-1180

[27] Modularity of 2-adic Barsotti-Tate representations [J].

Kisin, Mark .

INVENTIONES MATHEMATICAE, 2009, 178 (03) :587-634

[28]

Labesse J.-P., 2011, STABILIZATION TRACE, V1[44, P429

[29]

Newton J., 2020, J EUR MATH SOC

[30]

Newton J, 2021, PUBL MATH-PARIS, V134, P1, DOI 10.1007/s10240-021-00127-3

← 1 2 3 4 →