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

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry

Published online by Cambridge University Press:  11 December 2020

Ziyang Gao
Ziyang Gao*
Affiliation:
CNRS, IMJ-PRG, 4 place Jussieu, 75005Paris, [email protected] Department of Mathematics, Princeton University, Princeton, NJ08544, USA
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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 for studying the generic rank of the Betti map.

Keywords

Universal abelian varietyAx–Schanuelmixed Shimura varieties

MSC classification

Primary: 11G10: Abelian varieties of dimension $> 1$ 11G18: Arithmetic aspects of modular and Shimura varieties 14G35: Modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 156 , Issue 11 , November 2020 , pp. 2263 - 2297
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Copyright
© The Author(s) 2020

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