Cyclic coverings of the $p$-adic projective line by Mumford curves

Abstract

Exact bounds for the positions of the branch points for cyclic coverings of the $p$-adic projective line by Mumford curves are calculated in two ways. Firstly, by using Fumiharu Kato's *-trees, and secondly by giving explicit matrix representations of the Schottky groups corresponding to the Mumford curves above the projective line through combinatorial group theory.

17 pages, 3 eps-figures. To appear in manuscripta mathematica

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