Mumford Curves with Maximal Automorphism Group II: Lamé Type Groups in Genus 5-8

Abstract

A Mumford curve of genus g=5,6,7 or 8 over a non-Archimedean field ofcharacteristic p (such that if p=0, the residue field characteristic exceeds 5) has at most 12(g−1) automorphisms. In this paper, all curves that attain this bound and their automorphism groups (called of Lamé type) are explicitly determined.