# Tagged Questions

**4**

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**1**answer

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### 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,..)
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**14**

votes

**1**answer

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### 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 ...