Abstract.
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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Mathematics Subject Classification (2000): 11G20, 14H30, 14Q05
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Matignon, M. Vers un algorithme pour la réduction stable des revêtements p-cycliques de la droite projective sur un corps p-adique. Math. Ann. 325, 323–354 (2003). https://doi.org/10.1007/s00208-002-0387-4
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DOI: https://doi.org/10.1007/s00208-002-0387-4