Mixed Ax-Schanuel for the universal abelian varieties and some applications

Abstract

In this paper we prove the mixed Ax-Schanuel theorem for the universal abelian varieties (more generally any mixed Shimura variety of Kuga type), and give some simple applications. In particular we present an application to studying the generic rank of the Betti map.

Accepted to Compositio Mathematica. Comments are welcome

References in corpus (2)

• Ax-Schanuel for the j-function
• The Betti map associated to a section of an abelian scheme (with an appendix by Z. Gao)