ON THE IMAGE OF GALOIS l-ADIC REPRESENTATIONS FOR ABELIAN VARIETIES OF TYPE III

被引：14

作者：

Banaszak, Grzegorz ^{[1
]}

Gajda, Wojciech ^{[1
]}

Krason, Piotr ^{[2
]}

机构：

[1] Adam Mickiewicz Univ Poznan, Dept Math, PL-61614 Poznan, Poland

[2] Tech Univ Szczecin, Dept Math, PL-70415 Szczecin, Poland

来源：

TOHOKU MATHEMATICAL JOURNAL | 2010年 / 62卷 / 02期

关键词：

l-adic representation; abelian variety; Lie algebra; linear algebraic group; MUMFORD-TATE CONJECTURE; NUMBER-FIELDS; REAL MULTIPLICATIONS; HODGE CLASSES; FINITENESS; REDUCTION; POINTS;

D O I：

10.2748/tmj/1277298644

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate the image of the l-adic representation attached to the Tate module of an abelian variety defined over a number field. We consider simple abelian varieties of type III in the Albert classification. We compute the image of the l-adic and mod l Galois representations and we prove the Mumford-Tate and Lang conjectures for a wide class of simple abelian varieties of type III.

引用

页码：163 / 189

页数：27

共 38 条

[1]

[Anonymous], 2013, ALGEBRAIC GEOM

[2] On Galois representations for abelian varieties with complex and real multiplications [J].