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An ordinary abelian variety with an etale self-isogeny of p-power degree and no isotrivial factors

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Title: An ordinary abelian variety with an etale self-isogeny of p-power degree and no isotrivial factors
Authors: Helm, D
Item Type: Journal Article
Abstract: We construct, for every prime p, a function field K of characteristic p and an ordinary abelian variety A over K, with no isotrivial factors, that admits an ´etale self-isogeny φ : A → A of p-power degree. As a consequence, we deduce that there exist ordinary abelian varieties over function fields whose groups of points over the maximal purely inseparable extension is not finitely generated, answering in the negative a question of Thomas Scanlon.
Issue Date: 29-Sep-2022
Date of Acceptance: 21-Jul-2021
URI: http://hdl.handle.net/10044/1/90919
DOI: 10.4310/MRL.2022.v29.n2.a6
ISSN: 1073-2780
Start Page: 445
End Page: 454
Journal / Book Title: Mathematics Research Letters
Volume: 29
Issue: 2
Copyright Statement: © 2022 International Press of Boston, Inc. All rights reserved.
Publication Status: Published
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences
Mathematics