The universal Mumford curve, and its abelian differentials and periods in arithmetic formal geometry

Abstract

We construct the universal Mumford curve of given genus as a family of Mumford curves over the deformation space of degenerate curves in the category of arithmetic formal geometry. Furthermore, we give explicit formulas of abelian differentials and their periods of the universal Mumford curve.

arXiv comment16 pages, Revised version of arXiv:2010.11517v2 with some corrections and extensions