7,354 research outputs found
Perverse sheaves on Artin stacks
In this paper we develop the theory of perverse sheaves on Artin stacks
continuing the study in "The six operations for sheaves on Artin stacks I:
Finite Coefficients" and "The six operations for sheaves on Artin stacks II:
Adic Coefficients" (math.AG/0512097 and math.AG/0603680
Tame stacks in positive characteristic
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.Comment: 31 pages, 3 sections and 1 appendi
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