English

A non-archimedean Ax-Lindemann theorem

Algebraic Geometry 2018-01-08 v6 Logic Number Theory

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 PGL(2,Qpˉ)\mathop{\rm PGL}(2,\bar{\mathbf Q_p}) contained in PGL(2,Qˉ)\mathop{\rm PGL}(2,\bar{\mathbf Q}). In particular, we characterize bi-algebraic irreducible subvarieties of the uniformization.

Keywords

Cite

@article{arxiv.1511.03259,
  title  = {A non-archimedean Ax-Lindemann theorem},
  author = {Antoine Chambert-Loir and François Loeser},
  journal= {arXiv preprint arXiv:1511.03259},
  year   = {2018}
}

Comments

31 pages; revised version

R2 v1 2026-06-22T11:41:52.789Z