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D ( ) -affinité des schémas projectifs

Christine Huyghe (1998)

Annales de l'institut Fourier

Soient V un anneau de valuation discrète complet, d’inégales caractéristiques ( 0 , p ) , et 𝒳 un schéma formel projectif et lisse sur le spectre formel de V . Soit 𝒵 un diviseur ample sur 𝒳 et 𝒰 l’ouvert affine complémentaire du diviseur. Dans cette situation, P. Berthelot a construit sur 𝒳 un anneau d’opérateurs différentiels arithmétiques, à coefficients surconvergents le long de 𝒵 , noté D ( ) . Nous montrons ici que 𝒳 est D ( ) -affine. Ce résultat renforce l’intuition que la catégorie des D ( ) -modules cohérents est...

De Rham cohomology and homotopy Frobenius manifolds

Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette (2015)

Journal of the European Mathematical Society

We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.

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

Matthew Satriano (2012)

Annales de l’institut Fourier

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.

Decomposition numbers for perverse sheaves

Daniel Juteau (2009)

Annales de l’institut Fourier

The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial nilpotent orbit in a simple Lie algebra.This work has applications to modular representation theory, for Weyl groups using the nilpotent cone of the corresponding semisimple Lie algebra, and for reductive...

Deformations of free and linear free divisors

Michele Torielli (2013)

Annales de l’institut Fourier

We study deformations of free and linear free divisors. We introduce a complex similar to the de Rham complex whose cohomology calculates the deformation spaces. This cohomology turns out to be zero for all reductive linear free divisors and to be constructible for Koszul free divisors and weighted homogeneous free divisors.

Degree three cohomological invariants of semisimple groups

Alexander Merkurjev (2016)

Journal of the European Mathematical Society

We study the degree 3 cohomological invariants with coefficients in / ( 2 ) of a semisimple group over an arbitrary field. A list of all invariants of adjoint groups of inner type is given.

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