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

Algebraic stack Chow group of a stack Deligne–Mumford stack Glossary of algebraic geometry Pursuing Stacks Quotient space of an algebraic stack Ring of...

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...

theory of Teichmüller space Quotient stack - in a sense, this is the ultimate answer to the problem. Roughly, a "quotient prestack" is the category of...

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...

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...

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

{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...

[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...

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

groupoid; see groupoid scheme. Deligne–Mumford stacks are typically constructed by taking the stack quotient of some variety where the stabilizers are finite...

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...

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

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...

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...

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...

'\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 ]...

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...

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...

action of an algebraic group G on an algebraic variety X determines a quotient stack [X/G], which remembers the stabilizer subgroups for the action of G...

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

groups is equivalent in many situations to the Riemann–Roch theorem for quotient stacks by finite groups. One of the significant applications of the theorem...

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...

sheaves on the quotient stack [ X / G ] {\displaystyle [X/G]} . (Hence, the equivariant K-theory is a specific case of the K-theory of a stack.) A version...

Conrad, Brian (2005), The Keel–Mori theorem via stacks (PDF) Keel, Seán; Mori, Shigefumi (1997), "Quotients by groupoids", Annals of Mathematics, 2, 145...

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