Inventiones mathematicae

, Volume 141, Issue 1, pp 195–238 | Cite as

Déformations formelles des revêtements sauvagement ramifiés de courbes algébriques

  • José Bertin
  • Ariane Mézard
Article

Abstract.

In this paper we study formal moduli for wildly ramified Galois covering. We prove a local-global principle. We then focus on the infinitesimal deformations of the Z/pZ-covers. We explicitly compute a deformation of an automorphism of order p which implies a universal obstruction for p>2. By deforming Artin-Schreier equations we obtain a lower bound on the dimension of the local versal deformation ring. At last, by comparing the global versal deformation ring to the complete local ring in a point of a moduli space, we determine the dimensions of the global and local versal deformation rings.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • José Bertin
    • 1
  • Ariane Mézard
    • 1
  1. 1.Université de Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathématiques, B.P. 74, 38402 Saint-Martin d’Hères Cedex, France (e-mail: {jose.bertin, ariane.mezard}@ujf-grenoble.fr)France

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