, Volume 141, Issue 1, pp 195-238

Déformations formelles des revêtements sauvagement ramifiés de courbes algébriques

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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/p Z-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.

Oblatum 22-II-1999 & 15-XII-1999¶Published online: 29 March 2000