Number Theory Seminar
The Ax–Lindemann theorem is a functional algebraic independence statement, which is a geometric version of the classical Lindemann–Weierstrass theorem. Its generalizations to uniformizing maps of arithmetic varieties played a key role in recent progress on the André–Oort conjecture. In this talk I will present a non-archimedean 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.