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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.
We define the algebraic fundamental group π 1(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G↦ π1(G) is exact.
Let be a commutative -algebra where is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a -connection. Our result generalizes the classical Chern character from the -theory of to the algebraic De Rham cohomology.
Let be a finite extension over and the ring of integers. We prove the equivalence of categories between the category of Kisin modules of height 1 and the category of Barsotti-Tate groups over .
Dans cet article on étudie la transformation de Fourier-Deligne sur les schémas en groupes commutatifs unipotents connexes définis sur un corps parfait. On rappelle la construction du dual de Serre d’un groupe commutatif unipotent connexe et on définit la notion de paire duale admissible de schémas en groupes commutatifs unipotents connexes sur un corps parfait. On définit alors la transformation de Fourier-Deligne pour ces paires duales et on dégage les propriétés élémentaires de ce foncteur :...
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