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I'm trying to translate the Proj construction as a kind of quotient by a $\mathbb{G}_m$ action. Here's what I have so far: Let $X=Spec\,A$ be an affine scheme (after this case is setteled I imagine it ...

Let $G$ be a finite group and $k$ a field (alg. closed char 0 for simplicity). To every $G$ set $X$ we can assign the category of $G$-equivariant sheaves of $k$-vector spaces $Sh_G(X)$. It is ...

Let $H < G$ be a subgroup of a finite group $G$. Let $X:=G/H$ and $\mathcal{F} \in Sh_G(X)$ be an equivariant sheaf on $X$ (w.r.t. left multiplication) associated to a finite dimensional ...

This is a follow up question to this question which remained unanswered (satisfactorily) even after a large bounty. I have made a litlle progress and I have no a more specific question which might be ...

All sets and groups in the question are finite. In order to understand equivariant sheaves better I'm trying to prove some basic facts from Mackey theory using equivariant sheaves. The main obstacle ...