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Results tagged with tannakian-category
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user 5952
6
votes
Mumford-Tate groups and Hodge structures
Indeed. Look at Hodge structures as finite dimensional vector spaces $V$ over $\mathbb Q$ together with an action of the Deligne torus $\mathbb S$ on $V \otimes \mathbb C$, i.e. a morphism of algebrai …
- 4,015
3
votes
0
answers
316
views
When does Ext^2 vanish in a category of group representations.
Let $G$ be a linear algebraic group over field $k$ of characteristic zero. It is well known that the category of finite dimensional $k$--linear representations of $G$ is abelian, and that it is semisi …
- 4,015
9
votes
2
answers
512
views
Are algebraic groups defined by their invariants in tensor spaces?
Let $K$ be a field of characteristic zero, and let $G \subseteq \mathrm{GL}_V$ be an algebraic group over $K$, acting faithfully on a finite dimensional vector space $V$. Let $H \subseteq \mathrm{GL}_ …
- 4,015
7
votes
1
answer
486
views
About an embedding of abelian categories into categories of modules
Let $k$ be a field. Let $C$ be an abelian $k$-linear category with a symmetric tensor product $\otimes$ and internal homomorphisms, such that $\mathrm{End}(1)=k$. Let $M$ be another $k$-linear abelian …
- 4,015