de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities
Annales de l'Institut Fourier, Volume 62 (2012) no. 6, pp. 2013-2051.

We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic p (as defined by Abramovich, Olsson, and Vistoli) which lift mod p 2 degenerates. We push the result to the coarse spaces of such stacks, thereby obtaining a degeneracy result for schemes which are étale locally the quotient of a smooth scheme by a finite linearly reductive group scheme.

Nous démontrons que la suite spectrale de Hodge-De Rham d’un champ d’Artin propre modéré en caractéristique p (d’après Abramovich, Olsson et Vistoli) qui se relève mod p 2 dégénère. Nous étendons ce résultat à des schémas quotients d’un schéma lisse par un schéma en groupes linéaires réductifs.

DOI: 10.5802/aif.2741
Classification: 14A20, 14F40
Keywords: de Rham, Hodge, tame stack, linearly reductive
Mot clés : De Rham, Hodge, champs modéré, linéaire réductif
Satriano, Matthew 1

1 University of Michigan Department of Mathematics 2074 East Hall, Ann Arbor, MI 48109-1043 (USA)
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Satriano, Matthew. de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities. Annales de l'Institut Fourier, Volume 62 (2012) no. 6, pp. 2013-2051. doi : 10.5802/aif.2741. http://www.numdam.org/articles/10.5802/aif.2741/

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