Displaying similar documents to “Integral models for moduli spaces of G -torsors”

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...

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

Matthew Satriano (2012)

Annales de l’institut Fourier

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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.

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...

On the S-fundamental group scheme

Adrian Langer (2011)

Annales de l’institut Fourier

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We introduce a new fundamental group scheme for varieties defined over an algebraically closed (or just perfect) field of positive characteristic and we use it to study generalization of C. Simpson’s results to positive characteristic. We also study the properties of this group and we prove Lefschetz type theorems.

Whittaker and Bessel functors for G 𝕊 p 4

Sergey Lysenko (2006)

Annales de l’institut Fourier

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The theory of Whittaker functors for G L n is an essential technical tools in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence. We define Whittaker functors for G 𝕊 p 4 and study their properties. These functors correspond to the maximal parabolic subgroup of G 𝕊 p 4 , whose unipotent radical is not commutative. We also study similar functors corresponding to the Siegel parabolic subgroup of G 𝕊 p 4 , they are related with Bessel models for G 𝕊 p 4 and...