First vertices for generic Newton polygons, and $p$-cyclic coverings of the projective line

Abstract

In this paper we compute the first vertex of a generic Newton polygon in some special cases, and the corresponding Hasse polynomial. This allows us to show the nonexistence of $p$-cyclic coverings of the projective line in characteristic $p$ with supersingular jacobian for some (infinite families of) genera.

partial results, comments welcome

References in corpus (1)

• p-Density, exponential sums and Artin-Schreier curves

Cited by in corpus (3)

• The p-rank strata of the moduli space of hyperelliptic curves
• Hasse invariants and mod $p$ solutions of $A$-hypergeometric systems
• Families of Artin-Schreier curves with Cartier-Manin matrix of constant rank