Some families of supersingular Artin-Schreier curves in characteristic > 2

TL;DR

This paper proves that specific families of Artin-Schreier curves are supersingular in characteristics 5 and 7 using p-adic Dwork's method, expanding understanding of supersingularity in algebraic curves.

Contribution

It introduces a novel application of p-adic Dwork's method to establish supersingularity for particular families of Artin-Schreier curves.

Findings

Two families of Artin-Schreier curves are supersingular in characteristics 5 and 7.

The method confirms supersingularity for these curves for certain parameter values.

Advances the use of p-adic techniques in studying algebraic curve properties.

Abstract

In this short paper we prove that the following two 1-dimensional families of Artin-Schreier curves are supersingular: y^7 - y = x^5 + c.x^2 over F_7 y^5 - y = x^7 + c.x over F_5 (for some parameter c). Our method is developed upon the p-adic Dwork's method.