LOWER BOUNDS FOR RANKS OF MUMFORD-TATE GROUPS

被引：1

作者：

Orr, Martin ^{[1
]}

机构：

[1] Univ Paris 11, F-91400 Orsay, France

来源：

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE | 2015年 / 143卷 / 02期

关键词：

Abelian varieties; Mumford-Tate groups; ABELIAN-VARIETIES; REPRESENTATIONS;

D O I：

10.24033/bsmf.2684

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be a complex abelian variety and G its Mumford-Tate group. Supposing that the simple abelian subvarieties of A are pairwise non-isogenous, we find a lower bound for the rank rk G of G, which is a little less than log(2) dim A. If we suppose furthermore that End A is commutative, then we can improve this lower bound to rk G >= log(2) dim A + 2 and prove that this is sharp. We also obtain the same results for the rank of the l-adic monodromy group of an abelian variety defined over a number field.

引用

页码：229 / 246

页数：18

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