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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 algebraic fundamental group of a reductive group scheme over an arbitrary base scheme

Mikhail Borovoi, Cristian González-Avilés (2014)

Open Mathematics

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.

The Chern character for Lie-Rinehart algebras

Helge Maakestad (2005)

Annales de l'institut Fourier

Let $A$ be a commutative $S$ -algebra where $S$ is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras $L$ over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a $L$ -connection. Our result generalizes the classical Chern character from the $K$ -theory of $A$ to the algebraic De Rham cohomology.

The correspondence between Barsotti-Tate groups and Kisin modules when $p = 2$

Tong Liu (2013)

Journal de Théorie des Nombres de Bordeaux

Let $K$ be a finite extension over $ℚ_{2}$ and $𝒪_{K}$ 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 $𝒪_{K}$ .

The Fundamental Group-Scheme of an Abelian Variety.

Madhav V. Nori (1983)

Mathematische Annalen

The Picard-Vessiot closure in differential Galois theory

Andy R. Magid (2002)

Banach Center Publications

Théorie de Dieudonné sur un anneau de valuation parfait

Pierre Berthelot (1980)

Annales scientifiques de l'École Normale Supérieure

Théorie de Kummer-Artin-Schreier et applications

Noriyuki Suwa, Tsutomu Sekiguchi (1995)

Journal de théorie des nombres de Bordeaux

Transformation de Fourier-Deligne sur les groupes unipotents

Moussa Saibi (1996)

Annales de l'institut Fourier

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 :...

Displaying 1 – 9 of 9

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