The Chevalley-shephard-todd Theorem for Finite Linearly Reductive Group Schemes
نویسنده
چکیده
We generalize the classical Chevalley-Shephard-Todd theorem to the case of finite linearly reductive group schemes. As an application, we prove that every scheme X which is étale locally the quotient of a smooth scheme by a finite linearly reductive group scheme is the coarse space of a smooth tame Artin stack (as defined by Abramovich, Olsson, and Vistoli) whose stacky structure is supported on the singular locus of X.
منابع مشابه
N ov 2 00 8 EXTENDING THE COINVARIANT THEOREMS OF CHEVALLEY , SHEPHARD – TODD , MITCHELL , AND SPRINGER
We extend in several directions invariant theory results of Chevalley, Shephard and Todd, Mitchell and Springer. Their results compare the group algebra for a finite reflection group with its coinvariant algebra, and compare a group representation with its module of relative coinvariants. Our extensions apply to arbitrary finite groups in any characteristic.
متن کاملShephard-todd-chevalley Theorem for Skew Polynomial Rings
We prove the following generalization of the classical ShephardTodd-Chevalley Theorem. Let G be a finite group of graded algebra automorphisms of a skew polynomial ring A := kpij [x1, · · · , xn]. Then the fixed subring A has finite global dimension if and only if G is generated by quasireflections. In this case the fixed subring A is isomorphic a skew polynomial ring with possibly different pi...
متن کاملm at h . A C ] 2 4 M ay 2 00 8 EXTENDING THE COINVARIANT THEOREMS OF CHEVALLEY , SHEPHARD – TODD , MITCHELL , AND SPRINGER
We extend in several directions invariant theory results of Chevalley, Shephard and Todd, Mitchell and Springer. Their results compare the group algebra for a finite reflection group with its coinvariant algebra, and compare a group representation with its module of relative coinvariants. Our extensions apply to arbitrary finite groups in any characteristic.
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 کاملK-Theory Of Root Stacks And Its Application To Equivariant K-Theory
We give a definition of a root stack and describe its most basic properties. Then we recall the necessary background (Abhyankar’s lemma, Chevalley-Shephard-Todd theorem, Luna’s étale slice theorem) and prove that under some conditions a quotient stack is a root stack. Then we compute G-theory and K-theory of a root stack. These results are used to formulate the theorem on equivariant algebraic ...
متن کامل