Vers un algorithme pour la réduction stable des revêtements p-cycliques de la droite projective sur un corps p-adique

 In his Ph. D. thesis, C. Lehr offers an algorithm which gives the stable model for p-cyclic covers of the projective line over a p-adic field under the conditions that the branch locus whose cardinal is m+1 has the so called equidistant geometry and m<p. In this note we give an algorithm also in the equidistant geometry case but without condition on m. In particular we are able to study the reduction at 2 of hyperelliptic curves with equidistant branch locus.

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Vers un algorithme pour la réduction stable des revêtements p-cycliques de la droite projective sur un corps p-adique

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Received: 11 February 2002 / Revised version: 8 May 2002 / Published online: 2 December 2002

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Mathematics Subject Classification (2000): 11G20, 14H30, 14Q05