algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Geometrically, it generalizes a quotient of a scheme or a variety...
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Algebraic stack Chow group of a stack Deligne–Mumford stack Glossary of algebraic geometry Pursuing Stacks Quotient space of an algebraic stack Ring of...
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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...
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Group-scheme action (redirect from Quotient (algebraic geometry))
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...
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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...
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of an algebraic stack Quotient metric space Quotient object This disambiguation page lists articles associated with the title Quotient space. If an internal...
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In algebraic geometry, an affine GIT quotient, or affine geometric invariant theory quotient, of an affine scheme X = Spec A {\displaystyle X=\operatorname...
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{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...
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Equivariant cohomology (section Homotopy quotient)
can define the moduli stack of principal bundles Bun G ( X ) {\displaystyle \operatorname {Bun} _{G}(X)} as the quotient stack [ Ω / G ] {\displaystyle...
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Glossary of algebraic geometry (redirect from Good quotient)
[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...
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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...
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groupoid; see groupoid scheme. Deligne–Mumford stacks are typically constructed by taking the stack quotient of some variety where the stabilizers are finite...
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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...
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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...
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Lie group action (redirect from Quotient manifold)
stabilizers", M / G {\displaystyle M/G} becomes instead an orbifold (or quotient stack). An application of this principle is the Borel construction from algebraic...
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Derived scheme (section Stack quotients)
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...
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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...
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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...
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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...
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theory GIT quotient Groupoid scheme Group-scheme action Group-stack Invariant theory Quotient stack Raynaud, Michel (1967), Passage au quotient par une relation...
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'\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 ]...
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Moduli space (redirect from Moduli stack)
scheme Deformation theory GIT quotient Artin's criterion, general criterion for constructing moduli spaces as algebraic stacks from moduli functors Moduli...
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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...
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In mathematics, the quotient (also called Serre quotient or Gabriel quotient) of an abelian category A {\displaystyle {\mathcal {A}}} by a Serre subcategory...
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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...
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Riemann–Roch-type theorem (redirect from Riemann–Roch formula for stacks)
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...
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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...
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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...
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Conrad, Brian (2005), The Keel–Mori theorem via stacks (PDF) Keel, Seán; Mori, Shigefumi (1997), "Quotients by groupoids", Annals of Mathematics, 2, 145...
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equivalence. Differentiable stacks are particularly useful to handle spaces with singularities (i.e. orbifolds, leaf spaces, quotients), which appear naturally...
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