On the modularity of Q-curves

被引：25

作者：

Ellenberg, JS ^{[1
]}

Skinner, C

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

DUKE MATHEMATICAL JOURNAL | 2001年 / 109卷 / 01期

关键词：

D O I：

10.1215/S0012-7094-01-10914-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A Q-curve is an elliptic curve over a number field K which is geometrically isogenous to each of its Galois conjugates. K. Ribet [17] asked whether every Q-curve is modular and he showed that a positive answer would follow from J.-P Serre's conjecture on mod p Galois representations. We answer Ribet's question in the affirmative, subject to certain local conditions at 3.

引用

页码：97 / 122

页数：26

共 24 条

[1]

[Anonymous], 1971, KANO MEMORIAL LECT

[2]

BREUIL C, IN PRESS J AM MATH S

[3] Modularity of certain potentially Barsotti-Tate Galois representations [J].