Slope Estimates for Generalized Artin-Schreier Curves

TL;DR

This paper derives initial slope estimates for the Newton polygon of generalized Artin-Schreier curves using Frobenius and Verschiebung actions, leading to improved bounds on their point counts.

Contribution

It introduces new slope estimates for these curves and applies them to enhance the Hasse-Weil bound, advancing understanding of their arithmetic properties.

Findings

First slope estimates for Newton polygons of generalized Artin-Schreier curves

Application of Frobenius and Verschiebung actions on cohomology

Improved Hasse-Weil bounds for this class of curves

Abstract

We provide first slope estimates of the Newton polygon of generalized Artin-Schreier curves, which are proved using the action of Frobenius and Verschiebung on cohomology. We provide a number of applications such as an improved Hasse-Weil bound for this class of curves.