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

2018/06/04 by Ziyang Gao, Gao, Ziyang · 1 citation
Mathematics · #11G10 #11G18 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1806.01408

openalex publication_date 2018/06/04 · openalex created_date 2018/06/13 · openalex updated_date 2026/07/28

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.

Citations

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

Cited by

• Unlikely intersections in Shimura varieties and beyond: a survey

Related

• Ax-Schanuel for Shimura varieties
• Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results
• The Ax-Schanuel conjecture for variations of mixed Hodge structures
• On Special Subvarieties of the Universal Semi-abelian Scheme and Pink Conjectures
• Generic rank of Betti map and unlikely intersections