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Positivity of Hodge bundles of abelian varieties over some function fields

Part of: Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  03 August 2021

Xinyi Yuan
Xinyi Yuan*
Affiliation:
Beijing International Center for Mathematical Research, Peking University, Haidian District, Beijing100871, PR Chinayxy@bicmr.pku.edu.cn
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Abstract

The main result of this paper concerns the positivity of the Hodge bundles of abelian varieties over global function fields. As applications, we obtain some partial results on the Tate–Shafarevich group and the Tate conjecture of surfaces over finite fields.

Keywords

Hodge bundleample vector bundlefunction fieldheightabelian schemeNéron modelpurely inseparable pointstorsorsTate–Shafarevich groupBSD conjectureTate conjecture

MSC classification

Primary: 14G17: Positive characteristic ground fields
Secondary: 14G10: Zeta-functions and related questions (Birch-Swinnerton-Dyer conjecture) 14G25: Global ground fields
Type
Research Article
Information
Compositio Mathematica , Volume 157 , Issue 9 , September 2021 , pp. 1964 - 2000
Copyright
© 2021 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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