Displaying similar documents to “de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities”

Integral models for moduli spaces of G -torsors

Martin Olsson (2012)

Annales de l’institut Fourier

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Given a finite tame group scheme G , we construct compactifications of moduli spaces of G -torsors on algebraic varieties, based on a higher-dimensional version of the theory of twisted stable maps to classifying stacks.

Canonical integral structures on the de Rham cohomology of curves

Bryden Cais (2009)

Annales de l’institut Fourier

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For a smooth and proper curve X K over the fraction field K of a discrete valuation ring R , we explain (under very mild hypotheses) how to equip the de Rham cohomology H dR 1 ( X K / K ) with a : an R -lattice which is functorial in finite (generically étale) K -morphisms of X K and which is preserved by the cup-product auto-duality on H dR 1 ( X K / K ) . Our construction of this lattice uses a certain class of normal proper models of X K and relative dualizing sheaves. We show that our lattice naturally contains the lattice...

Decomposition numbers for perverse sheaves

Daniel Juteau (2009)

Annales de l’institut Fourier

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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,...

The fundamental groupoid scheme and applications

Hélène Esnault, Phùng Hô Hai (2008)

Annales de l’institut Fourier

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We define a linear structure on Grothendieck’s arithmetic fundamental group π 1 ( X , x ) of a scheme X defined over a field k of characteristic 0. It allows us to link the existence of sections of the Galois group Gal ( k ¯ / k ) to π 1 ( X , x ) with the existence of a neutral fiber functor on the category which linearizes it. We apply the construction to affine curves and neutral fiber functors coming from a tangent vector at a rational point at infinity, in order to follow this rational point in the universal covering...

The Drinfeld Modular Jacobian J 1 ( n ) has connected fibers

Sreekar M. Shastry (2007)

Annales de l’institut Fourier

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We study the integral model of the Drinfeld modular curve X 1 ( n ) for a prime n ∈ 𝔽 q [ T ] . A function field analogue of the theory of Igusa curves is introduced to describe its reduction mod n . A result describing the universal deformation ring of a pair consisting of a supersingular Drinfeld module and a point of order n in terms of the Hasse invariant of that Drinfeld module is proved. We then apply Jung-Hirzebruch resolution for arithmetic surfaces to produce a regular model of X 1 ( n ) which, after contractions...