Jun 1, 2023 · The quotient stack of the action of G G on X X is a stack 𝒟 \mathcal{D} equipped with a principal G G-bundle of stacks X ̲ → 𝒟 \underline{X}\rightarrow \mathcal{D} such that any …

A stack-theoretic proof of Luna's étale slice theorem is presented proving that for stacks $\mathcal{X} = [\mathop{\mathrm{Spec}}(A)/G]$ with $G$ linearly reductive, then étale locally …

Feb 9, 2022 · This comes (by ``looping") from an action of a 2-group (or group-stack) $BJ$ on the stack $V/G$, and the quotient is an honest 2-stack.

The quotient stack \[ p : [U/R] \longrightarrow (\mathit{Sch}/S)_{fppf} \] of $(U, R, s, t, c)$ is the stackification (see Stacks, Lemma 8.9.1 ) of the category fibred in groupoids $[U/_{\! p}R]$ …

A differentiable stack is the analogue in differential geometry of an algebraic stack in algebraic geometry. It can be described either as a stack over differentiable manifolds which admits an …

Mar 8, 2022 · Consider the quotient stack $[X/G]$ for $G$ a finite group. This is a Deligne--Mumford stack. Is there a definition of a version of euler characteristic of DM stacks so that $$...

quotient stack Usually denoted by [X/G], a quotient stack generalizes a quotient of a scheme or variety.

The quotient stack $[X/G]$ is an algebraic stack if and only if there exists a morphism of algebraic spaces $\varphi : X' \to X$ such that $G \times _ B X' \to X$, $(g, x') \mapsto a(g, \varphi (x'))$ …

In algebraic geometry, the Chow group of a stack is a generalization of the Chow group of a variety or scheme to stacks. For a quotient stack = [/], the Chow group of X is the same as the …

In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory.

A special case of the construction above is the quotient stack \[ [X/G] \longrightarrow (\mathit{Sch}/S)_{fppf} \] associated to a datum $(B, G/B, m, X/B, a)$.