Degeneracy loci in the universal family of Abelian varieties

verfasst von

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Universität Basel

Typ

Artikel

Journal

Journal of number theory

Anzahl der Seiten

26

ISSN

0022-314X

Publikationsdatum

27.06.2024

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie

Elektronische Version(en)

https://doi.org/10.1016/j.jnt.2024.05.015 (Zugang: Offen)