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.
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页码：97 / 122
页数：26
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