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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 …

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 …

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 …

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 representatio …

$\DeclareMathOperator\Sym{Sym}$Let $G$ be a compact lie group. Chern–Weil theory tells us that there's a homomorphism: $$H^{*}(BG;\mathbb{R}) \to (\Sym^{\bullet} \mathfrak{g^*})^G$$ which in our case …

Let $R$ be a regular ring over a field of char 0. Let $X=Spec R$ and $D=\mathcal{D}_X$ the algebra of differential operators over it. The overall vague question is what kind of algebraic object is $ …

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 essenti …

Let $C$ be a smooth projective curve over an algebraically closed field $k$. The tangent lie algeborid $\mathcal{T}_C$ of $C$ is just sheaf of vector fields on $C$ equipped with the usual lie bracke …

I believe there has been at least one question similar to this one and yet I still think this particular question deserves to have a thread of its own. I'm becoming increasingly fascinated by stuff r …