Padic Schwarzian triangle groups of Mumford type
Abstract
In this article we discuss a certain padic analogue of classical Schwarzian triangle groups, an analogue which is related to Mumford's uniformization of padic analytic curves. padic Schwarzian triangle groups are defined to be the Galois groups of analytic coverings over projective line with precisely 3 branch points. We say that a padic triangle group is of Mumford type if the corresponding universal covering is given by a certain locally compact analytic subspace in projective line, related to Mumford's uniformization. The main theorem provides a complete classification of padic triangle groups of Mumford type; our list of these groups contains some of the arithmetic padic triangle groups which are discussed by Yves Andre. Notably, we deduce that padic triangle groups of Mumford type exist only if p=2,3,5.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 1999
 arXiv:
 arXiv:math/9908174
 Bibcode:
 1999math......8174K
 Keywords:

 Algebraic Geometry;
 Group Theory
 EPrint:
 28 pages, 26 figures