Tame stacks in positive characteristic

Details Tame stacks in positive characteristic Tame stacks in positive characteristic

2007-03-11

arxiv.org/abs/math/0703310v1

Mathematics

Algebraic Geometry

31 pages, 3 sections and 1 appendix

Scientific paper

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. In a subsequent paper we will show that tame algebraic stacks admit a good theory of stable maps.

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