4
votes
1answer
566 views

Mumford-Tate groups and Hodge structures

It is well known that the Mumford-Tate group of a polarizable pure $Q$-Hodge structure is reductive. (this is proved for instance in Deligne et al LNM 900, Voisin's books on Algebraic Geometry,..) ...
14
votes
1answer
474 views

Semistable filtered vector spaces, a Tannakian category.

Let $k$ be a field (char = 0, perhaps). Let $(V,F)$ be a pair, where $V$ is a finite-dimensional $k$-vector space, and $F$ is a filtration of $V$, indexed by rational numbers, satisfying: $F^i V ...