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Integral models for moduli spaces of G -torsors

Martin Olsson — 2012

Annales de l’institut Fourier

Given a finite tame group scheme G , we construct compactifications of moduli spaces of G -torsors on algebraic varieties, based on a higher-dimensional version of the theory of twisted stable maps to classifying stacks.

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

Yves LaszloMartin 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.

Tame stacks in positive characteristic

Dan AbramovichMartin OlssonAngelo 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.

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