Quotient stack information

algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Geometrically, it generalizes a quotient of a scheme or a variety...

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 X = [ Y / G ] {\displaystyle...

the stack B G {\displaystyle BG} is algebraictheorem 6.1. Gerbe Chow group of a stack Cohomology of a stack Quotient stack Sheaf on an algebraic stack Toric...

of an algebraic stack Quotient metric space Quotient object This disambiguation page lists articles associated with the title Quotient space. If an internal...

can define the moduli stack of principal bundles Bun G ⁡ ( X ) {\displaystyle \operatorname {Bun} _{G}(X)} as the quotient stack [ Ω / G ] {\displaystyle...

{Bun} _{G}(X)} as the quotient stack of the space of holomorphic connections on X by the gauge group. Replacing the quotient stack (which is not a topological...

In algebraic geometry, an affine GIT quotient, or affine geometric invariant theory quotient, of an affine scheme X = Spec ⁡ A {\displaystyle X=\operatorname...

Related Areas (2)), 34. Springer-Verlag, Berlin, 1994. xiv+292 pp. MR1304906 ISBN 3-540-56963-4 Quotient by an equivalence relation Quotient stack v t e...

[X/G] The quotient stack of, say, an algebraic space X by an action of a group scheme G. X / / G {\displaystyle X/\!/G} The GIT quotient of a scheme...

m and G is an algebraic group of dimension n acting on V, then the quotient stack [V/G] has dimension m − n. The Krull dimension of a commutative ring...

In algebraic geometry, the quotient space of an algebraic stack F, denoted by |F|, is a topological space which as a set is the set of all integral substacks...

yields the correct (virtual) dimension of the quotient stack. In particular, if we look at the moduli stack of principal G {\displaystyle G} -bundles, then...

stacks. In the category of stacks we can form even more quotients by group actions than in the category of algebraic spaces (the resulting quotient is...

stabilizers", M / G {\displaystyle M/G} becomes instead an orbifold (or quotient stack). An application of this principle is the Borel construction from algebraic...

coarser than the Chow group of a stack. The cohomology of a quotient stack (e.g., classifying stack) can be thought of as an algebraic counterpart of equivariant...

Gordan's lemma Toric ideal Toric stack (roughly this is obtained by replacing the step of taking a GIT quotient by a quotient stack) Toroidal embedding...

'\end{aligned}}} Then, the moduli stack of elliptic curves over C {\displaystyle \mathbb {C} } is given by the stack quotient M 1 , 1 ≅ [ SL 2 ( Z ) ∖ h ]...

theory GIT quotient Groupoid scheme Group-scheme action Group-stack Invariant theory Quotient stack Raynaud, Michel (1967), Passage au quotient par une relation...

scheme Deformation theory GIT quotient Artin's criterion, general criterion for constructing moduli spaces as algebraic stacks from moduli functors Moduli...

of taking GIT quotients with that of taking quotient stacks. Consequently, a toric variety is a coarse approximation of a toric stack. A toric orbifold...

taking an element s ∈ A {\displaystyle s\in A} . Then, the stack is given by the stack quotient ( L , s ) / S r = [ Spec ( B ) / μ r ] {\displaystyle {\sqrt[{r}]{(L...

In mathematics, the quotient (also called Serre quotient or Gabriel quotient) of an abelian category A {\displaystyle {\mathcal {A}}} by a Serre subcategory...

equivalence. Differentiable stacks are particularly useful to handle spaces with singularities (i.e. orbifolds, leaf spaces, quotients), which appear naturally...