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2020 On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic, II
Damian Rössler
Algebra Number Theory 14(5): 1123-1173 (2020). DOI: 10.2140/ant.2020.14.1123

Abstract

Let A be an abelian variety over the function field K of a curve over a finite field. We describe several mild geometric conditions ensuring that the group A ( K perf ) is finitely generated and that the p -primary torsion subgroup of A ( K sep ) is finite. This gives partial answers to questions of Scanlon, Ghioca and Moosa, and Poonen and Voloch. We also describe a simple theory (used to prove our results) relating the Harder–Narasimhan filtration of vector bundles to the structure of finite flat group schemes of height one over projective curves over perfect fields. Finally, we use our results to give a complete proof of a conjecture of Esnault and Langer on Verschiebung divisibility of points in abelian varieties over function fields.

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Damian Rössler. "On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic, II." Algebra Number Theory 14 (5) 1123 - 1173, 2020. https://doi.org/10.2140/ant.2020.14.1123

Information

Received: 20 September 2018; Revised: 19 November 2019; Accepted: 17 December 2019; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07244792
MathSciNet: MR4129384
Digital Object Identifier: 10.2140/ant.2020.14.1123

Subjects:
Primary: 11J95
Secondary: 11G10 , 14G25

Keywords: abelian varieties , frobenius , purely inseparable extensions , rational points , Verschiebung

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 5 • 2020
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