Martin Orr's Blog

Mumford-Tate groups

Posted by Martin Orr on Monday, 04 October 2010 at 12:37

In this post I will define the Mumford-Tate group of an abelian variety. This is a \mathbb{Q}-algebraic group, such that the Hodge structure is a representation of this group. The Mumford-Tate group is important in the study of Hodge theory, and surprisingly also tells us things about the \ell-adic representations attached to the abelian variety.

4 comments Tags abelian-varieties, alg-geom, alg-groups, hodge, maths