Degeneracy loci in the universal family of Abelian varieties

authored by

Ziyang Gao, Philipp Habegger

Abstract

Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in certain mixed Shimura varieties. In this expository note we revisit some of these results while minimizing the use of mixed Shimura varieties while working in a family of principally polarized abelian varieties. We also explain their relevance for applications in diophantine geometry.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

University of Basel

Type

Article

Journal

Journal of number theory

No. of pages

26

ISSN

0022-314X

Publication date

27.06.2024

Publication status

E-pub ahead of print

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://doi.org/10.1016/j.jnt.2024.05.015 (Access: Open)