# Discontinuous groups in positive characteristic and automorphisms of Mumford curves

@article{Cornelissen1999DiscontinuousGI,
title={Discontinuous groups in positive characteristic and automorphisms of Mumford curves},
author={Gunther Cornelissen and Fumiharu Kato and Aristeides Kontogeorgis},
journal={Mathematische Annalen},
year={1999},
volume={320},
pages={55-85}
}
• Published 31 August 1999
• Mathematics
• Mathematische Annalen
A Mumford curve of genus g (>1) over a non-archimedean valued field k of positive characteristic has at most max{12(g-1), 2 g^(1/2) (g^(1/2)+1)^2} automorphisms. This bound is sharp in the sense that there exist Mumford curves of arbitrary high genus that attain it (they are fibre products of suitable Artin-Schreier curves). The proof provides (via its action on the Bruhat-Tits tree) a classification of discontinuous subgroups of PGL(2,k) that are normalizers of Schottky groups of Mumford…
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We compute the dimension of the tangent space to, and the Krull dimension of the pro-representable hull of two deformation functors. The first one is the "algebraic" deformation functor of an
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