Discontinuous groups in positive characteristic and automorphisms of Mumford curves

Cornelissen, Gunther and Kato, Fumiharu and Kontogeorgis, Aristides

Abstract

In this paper, we prove that the order of the automorphism group of a Mumford curve in positive characteristic is bounded by a cubic polynomial of square-root of its genus, and moreover, this bound is sharp. We also show that the automorphisms of Drinfeld modular curves (with the full level) are, under some conditions on the characteristic, all modular in the sense that they come from the normalizer of the corresponding modular group