On abelian surfaces with potential quaternionic multiplication

被引：4

作者：

Dieulefait, LV

Rotger, V

机构：

[1] Univ Barcelona, Dept Algebra & Geometria, Barcelona 08007, Spain

[2] Univ Politecn Catalunya, Dept Matemat Aplicada 4, EUPVG, Vilanova I La Geltru, Spain

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2005年 / 12卷 / 04期

关键词：

abelian surface; Galois representation; quaternion algebra; modularity;

D O I：

10.36045/bbms/1133793348

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An abelian surface A over a field K has potential quaternionic multiplication if the ring End((K) over bar)(A) of geometric endomorphisms of A is an order in an indefinite rational division quaternion algebra. In this brief note, we study the possible structures of the ring of endomorphisms of these surfaces and we provide explicit examples of Jacobians of curves of genus two which show that our result is sharp.

引用

页码：617 / 624

页数：8

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