# Martin's Blog

## Motivic Galois groups and periods

Posted by Martin Orr on Tuesday, 03 November 2015 at 16:00

In my last post, I discussed how the existence of a polarisation implies an upper bound for the transcendence degree of the extended period matrix of an abelian variety, namely the dimension of the general symplectic group (where is the dimension of the abelian variety). In this post, I will discuss how this can be generalised to take into account all algebraic cycles on the abelian variety. The group is replaced by the motivic Galois group of the abelian variety, which I will define. I will also mention how Deligne's theorem on absolute Hodge cycles allows us to replace the motivic Galois group by the Mumford-Tate group.