# Tagged Questions

The tag has no usage guidance.

316 views

### Deligne's theorem on the characterisation of Tannakian categories

I am trying to understand the proof of the Theorem 7.1 from Catégories Tannakiennes by Pierre Deligne https://publications.ias.edu/sites/default/files/60_categoriestanna.pdf. Essentially, it is ...
210 views

### Relationship between $\mathcal{D}$ - modules, Tannakian formalism and Galois theory of monodromy representations

Is there a relationship between $\mathcal{D}$ - modules, Tannakian formalism and Galois theory of monodromy representations ? Thanks in advance for your help.
70 views

### Chevalley property for Tannakian categories

Are all Tannakian categories have the Chevalley property? I know that the categories $\mathrm{Rep}_k(G)$ have the Chevalley property for affine algebraic groups $G$ over a field $k$, but I don't know ...
119 views

169 views

### Faithful exact functors to tensor categories

Let $P$ be a "nice" $k$-linear abelian tensor category (e.g. A tannakian category or a fusion category over a field $k$) and $F: M\to P$ an additive $k$-linear exact and faithful functor. I want to ...
117 views

### Galois group - unknown word

I found in some articles a definition of the Galois group of a differential module. In the definition appeared the expression $(Repr(Gal(M,\nabla),Forget)$. According to the the articles, this pair ...
279 views

### What is the role of fiber functor in Deligne's theorem on Tannakian categories?

The theorem states that, for a field $k$ of characteristic 0, any $k$-linear tensor category with $End(1)=k$ satisfying a condition that each object is annihilated by a Schur functor, is equivalent to ...
451 views

### Exact sequences of groups and Tannakian formalism

By work of Deligne and others (I am following Deligne-Milne's notes which I just began to read: http://www.jmilne.org/math/xnotes/tc.pdf) we know that a given affine group scheme G can be recovered ...
671 views

374 views

### automorphism of fibre functors

If $G$ is an affine group scheme over a field $k$, then we have the forgetful functor $\omega$ from the category ${\rm Rep}_k(G)$ of finite representations of $G$ to the category of finite dimensional ...
282 views

### Counter example in Tannaka reconstruction?

This question is motivated by my attempts to answer the question Invariants for the exceptional complex simple Lie algebra $F_4$ from the point of view of Tannaka reconstruction. This has led me to ...