de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities

Satriano, Matthew

Annales de l'Institut Fourier, Tome 62 (2012) no. 6, pp. 2013-2051.

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.

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.

Classification : 14A20, 14F40
Keywords: de Rham, Hodge, tame stack, linearly reductive
Mot clés : De Rham, Hodge, champs modéré, linéaire réductif

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