Displaying similar documents to “Canonical integral structures on the de Rham cohomology of curves”

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.

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.

Galois actions on Néron models of Jacobians

Lars H. Halle (2010)

Annales de l’institut Fourier

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Let X be a smooth curve defined over the fraction field K of a complete discrete valuation ring R . We study a natural filtration of the special fiber of the Néron model of the Jacobian of X by closed, unipotent subgroup schemes. We show that the jumps in this filtration only depend on the fiber type of the special fiber of the minimal regular model with strict normal crossings for X over R , and in particular are independent of the residue characteristic. Furthermore, we obtain information...

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...

Stable twisted curves and their r -spin structures

Alessandro Chiodo (2008)

Annales de l’institut Fourier

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The subject of this article is the notion of r -spin structure: a line bundle whose r th power is isomorphic to the canonical bundle. Over the moduli functor M g of smooth genus- g curves, r -spin structures form a finite torsor under the group of r -torsion line bundles. Over the moduli functor M ¯ g of stable curves, r -spin structures form an étale stack, but both the finiteness and the torsor structure are lost. In the present work, we show how this bad picture can be definitely...