A non-archimedean Ax-Lindemann theorem

Abstract

We prove a statement of Ax-Lindemann type for the uniformization of products of Mumford curves whose associated fundamental groups are non-abelian Schottky subgroups of $\mathrm{PGL}(2,\overline{{\mathbf{Q}}_p})$ contained in $\mathrm{PGL}(2,\bar{\mathbf{Q}})$. In particular, we characterize bi-algebraic irreducible subvarieties of the uniformization.

31 pages; revised version

Cited by in corpus (3)

• Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fields
• Absolute sets and the Decomposition Theorem
• Cohomology jump loci of quasi-compact Kähler manifolds