Double Artin-Schreier extensions of rational function fields with many lifted automorphisms

TL;DR

This paper explores double Artin-Schreier extensions of rational function fields in positive characteristic, constructing new function fields with large automorphism groups relative to their genus.

Contribution

It introduces new families of ordinary function fields obtained via double Artin-Schreier extensions and determines their full automorphism groups, extending known automorphism group bounds.

Findings

Constructed new families of function fields with large automorphism groups

Determined the full automorphism groups of these new function fields

Showed these groups are large relative to the genus

Abstract

In this paper we investigate algebraic function fields in positive characteristic mainly obtained as double Artin-Schreier extensions of rational function fields with a plane model. The goal is to extend to such extensions large automorphism groups of the rational function field. In this way, we construct some new families of ordinary function fields and determine their full automorphism groups. Such groups are large with respect to the genus, compared with the known upper bounds on the size of the automorphism group of an ordinary function field.