A non-archimedean Ax-Lindemann theorem

By François Loeser (Sorbonne Université)
Abstract: The Ax-Lindemann theorem is a functional algebraic independence statement, which is a geometric version of the classical Lindemann-Weierstrass theorem. Itsgeneralizations to uniformizing maps of arithmetic varieties played a key role in recent progress on the Andr´e-Oort conjecture. In this talk I will present a nonarchimedean analogue for the uniformization of products of Mumford curves. In particular, we characterize bi-algebraic irreducible subvarieties of the uniformization.
This is joint work with Antoine Chambert-Loir.