Modularity of GL2(Fp)-representations over CM fields

被引：0

作者：

Allen, Patrick B. ^{[1
]}

Khare, Chandrashekhar ^{[2
]}

Thorne, Jack A. ^{[3
]}

机构：

[1] Dept Math & Stat, Burnside Hall,805 Sherbrooke St West, Montreal, PQ H3A 0B9, Canada

[2] Univ Calif Los Angeles, Dept Math, 6363 Math Sci Bldg ,520 Portola Pl, Los Angeles, CA 90095 USA

[3] DPMMS, Wilberforce Rd, Cambridge CB3 0WB, England

来源：

CAMBRIDGE JOURNAL OF MATHEMATICS | 2023年 / 11卷 / 01期

基金：

欧洲研究理事会; 加拿大自然科学与工程研究理事会;

关键词：

Galois representations; Modularity of elliptic curves; COHOMOLOGY; REPRESENTATIONS; AUTOMORPHY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that many representations ? : Gal(K/K) ? GL(2)(F-3), where K is a CM field, arise from modular elliptic curves. We prove similar results when the prime p = 3 is replaced by p = 2 or p = 5. As a consequence, we prove that a positive proportion of elliptic curves over any CM field not containing a 5th root of unity are modular.

引用

页码：1 / 158

页数：158

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