Martin's Blog

Images of Galois representations

Posted by Martin Orr on Saturday, 27 November 2010 at 16:22

In this post, I will continue to talk about the \ell-adic representations attached to abelian varieties, and in particular the images G_\ell of these representations. I will define algebraic groups approximating G_\ell, which are often more convenient to work with. I will end by stating the Mumford-Tate conjecture, linking G_\ell to the Mumford-Tate group.

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

Tate modules

Posted by Martin Orr on Sunday, 21 November 2010 at 17:32

I said after my last post that I would write something about \ell-adic representations coming from abelian varieties. I have finally got around to doing so: here I will tell the story of how these representations are defined, and show that the Tate module is canonically isomorphic to H_1(A, \mathbb{Z}) \otimes \mathbb{Z}_\ell. Next time I will relate this to Mumford-Tate groups.

2 comments Tags abelian-varieties, alg-geom, maths, number-theory