They define maps $d_0,d_1,d_2,$ and $s_0$, and then say that a $G$-equivariant sheaf on $X$ is a pair $(F,\theta)$, where $F$ is a sheaf on $X$ and $\theta$ is an isomorphism …

A $G$-equivariant quasi-coherent $\mathcal{O}_ X$-module, or simply an equivariant quasi-coherent $\mathcal{O}_ X$-module, is a pair $(\mathcal{F}, \alpha )$, where $\mathcal{F}$ is …

Two basic examples of equivariant sheaves we will be considering: • The sheaf of G-invariant functions on X. • O(V), the sheaf of sections of an equivariant vector bundle V → X.

Nov 1, 2022 · If you're dealing with coherent sheaves, you should consider the category $\mathcal{D}^b(X)^{G}$ of $G$-equivariant coherent sheaves. Note that the isomorphism …

Mar 21, 2019 · This question concerns the meaning of the data defining a so called equivariant sheaf $F$ on a scheme X. Let denote by $\sigma: G \times_S X \to X$ an action of a group …

Equivariant maps generalize the concept of invariants, functions whose value is unchanged by a symmetry transformation of their argument. The value of an equivariant map is often …

In algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Geometrically, it generalizes a quotient of a scheme or a variety by a group: a quotient variety, …

Oct 27, 2015 · Let C be a site, let µ be a sheaf of groups on C. Can someone explain me what does a µ-equivariant morphism of sheaves on C means ? I understand the definition of …

The equivariant derived category of sheaves is introduced. All usual functors on sheaves are extended to the equivariant situation. Some applications to the equivariant intersection …

1. Equivariant Sheaves 1.1. General definitions. Suppose a linear algebraic group G acts on a variety X. What is an equivariant sheaf on X? As motivation, we first give the definition of a …

Mar 27, 2019 · I have a question about the data defining the equivariant sheaf $F$ on a scheme X from wiki: https://en.wikipedia.org/wiki/Equivariant_sheaf. Denote by $\sigma: G \times_S X \to …

Dec 25, 2012 · What is the best introduction (textbook) to equivariant sheaves on algebraic varieties equipped with an action of an algebraic group?

Abstract: For certain tame abelian covers of arithmetic surfaces X/Y we obtain striking formulas, involving a quadratic form derived from intersection numbers, for the equivariant Euler …

Consider category of $G$ equivariant sheaves $\mathcal{Sh}_G (X)$. Denote by $\Gamma_G := Inv \circ \Gamma$ composition of two functors. I.e. we are taking global section of an …