7,409 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
Nagata compactification for algebraic spaces
We prove the Nagata compactification theorem for any separated map of finite
type between quasi-compact and quasi-separated algebraic spaces, generalizing
earlier results of Raoult. Along the way we also prove (and use) absolute
noetherian approximation for such algebraic spaces, generalizing earlier
results in the case of schemes.Comment: 49 pages, various clarifications and bugfixe
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