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Tame stacks in positive characteristic

Dan Abramovich, Martin Olsson, Angelo Vistoli (2008)

Annales de l’institut Fourier

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 étale locally quotient by actions of linearly reductive finite group schemes.

The six operations for sheaves on Artin stacks I: Finite coefficients

Yves Laszlo, Martin Olsson (2008)

Publications Mathématiques de l'IHÉS

In this paper we develop a theory of Grothendieck’s six operations of lisse-étale constructible sheaves on Artin stacks locally of finite type over certain excellent schemes of finite Krull dimension. We also give generalizations of the classical base change theorems and Kunneth formula to stacks, and prove new results about cohomological descent for unbounded complexes.

The structure of a local embedding and Chern classes of weighted blow-ups

Anca M. Mustaţǎ, Andrei Mustaţǎ (2012)

Journal of the European Mathematical Society

For a proper local embedding between two Deligne-Mumford stacks Y and X , we find, under certain mild conditions, a new (possibly non-separated) Deligne-Mumford stack X ' , with an etale, surjective and universally closed map to the target X , and whose fiber product with the image of the local embedding is a finite union of stacks with corresponding etale, surjective and universally closed maps to Y . Moreover, a natural set of weights on the substacks of X ' allows the construction of a universally closed...

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