We introduce and study a class of algebraic stacks with finite inertia in positive and mixed characteristic, which we call tame algebraic stacks. They include tame Deligne-Mumford stacks, and are arguably better behaved than general Deligne-Mumford stacks. We also give a complete characterization of finite flat linearly reductive schemes over an arbitrary base. Our main result is that tame algebraic stacks are etale locally quotient by actions of linearly reductive finite group schemes.

Tame stacks in positive characteristic

VISTOLI, ANGELO
2008

Abstract

We introduce and study a class of algebraic stacks with finite inertia in positive and mixed characteristic, which we call tame algebraic stacks. They include tame Deligne-Mumford stacks, and are arguably better behaved than general Deligne-Mumford stacks. We also give a complete characterization of finite flat linearly reductive schemes over an arbitrary base. Our main result is that tame algebraic stacks are etale locally quotient by actions of linearly reductive finite group schemes.
2008
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/6472
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