On the Local Quotient Structure of Artin Stacks
نویسنده
چکیده
We show that near closed points with linearly reductive stabilizer, Artin stacks are formally locally quotient stacks by the stabilizer and conjecture that the statement holds étale locally. In particular, we prove that if the stabilizer of a point is linearly reductive, the stabilizer acts algebraically on a miniversal deformation space generalizing results of Pinkham and Rim.
منابع مشابه
Local Properties of Good Moduli Spaces
We study the local properties of Artin stacks and their good moduli spaces, if they exist. We show that near closed points with linearly reductive stabilizer, Artin stacks formally locally admit good moduli spaces. We also give conditions for when the existence of good moduli spaces can be deduced from the existence of étale charts admitting good moduli spaces.
متن کاملCanonical Artin Stacks over Log Smooth Schemes
We develop a theory of toric Artin stacks extending the theories of toric Deligne-Mumford stacks developed by Borisov-Chen-Smith, Fantechi-Mann-Nironi, and Iwanari. We also generalize the Chevalley-Shephard-Todd theorem to the case of diagonalizable group schemes. These are both applications of our main theorem which shows that a toroidal embedding X is canonically the good moduli space (in the...
متن کاملRiemann-roch for Deligne-mumford Stacks
We give a simple proof of the Riemann-Roch theorem for Deligne-Mumford stacks using the equivariant Riemann-Roch theorem and the localization theorem in equivariant K-theory, together with some basic commutative algebra of Artin local rings.
متن کاملThe Cotangent Stack
1.2. We refer to [LMB] for the basic background on stacks. Let us quickly recall: a stack over a scheme S is a sheaf of groupoids on the faithfully flat topology of S-schemes, where the presheaf requirement that the composition of the restriction maps is the restriction map of the composition is understood in the weak sense. Stacks form a 2-category with fiber products and there is a clear embe...
متن کاملA Luna Étale Slice Theorem for Algebraic Stacks
We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is étale-locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group. The proof uses an equivariant version of Artin’s algebraization theorem proved in the appendix. We provide numerous applications of the main theorems.
متن کامل