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September 2020 Extending finite-subgroup schemes of semistable abelian varieties via log-abelian varieties
Heer Zhao
Kyoto J. Math. 60(3): 895-910 (September 2020). DOI: 10.1215/21562261-2019-0049

Abstract

We show—for a semistable abelian variety A K over a complete discrete valuation field K —that every finite-subgroup scheme of A K extends to a log finite-flat group scheme over the valuation ring of K endowed with the canonical log structure. To achieve this, we first give a positive answer to a question of Nakayama, namely whether every weak log-abelian variety over an fs (fine and saturated) log scheme with its underlying scheme locally noetherian is a sheaf for the Kummer-flat topology. We also give several equivalent conditions defining isogenies of log-abelian varieties.

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Heer Zhao. "Extending finite-subgroup schemes of semistable abelian varieties via log-abelian varieties." Kyoto J. Math. 60 (3) 895 - 910, September 2020. https://doi.org/10.1215/21562261-2019-0049

Information

Received: 25 August 2017; Revised: 23 January 2018; Accepted: 29 January 2018; Published: September 2020
First available in Project Euclid: 12 August 2020

MathSciNet: MR4134352
Digital Object Identifier: 10.1215/21562261-2019-0049

Subjects:
Primary: 14K99
Secondary: 11G99, 14D06

Rights: Copyright © 2020 Kyoto University

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Vol.60 • No. 3 • September 2020
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