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arXiv · 1909.01038

Extending finite subgroup schemes of semi-stable abelian varieties via log abelian varieties

Heer Zhao
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Abstract

For a semi-stable abelian variety A_K over a complete discrete valuation field K, we show 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 prove that every weak log abelian variety over an fs log scheme with its underlying scheme locally noetherian, is a sheaf for the Kummer flat topology, which answers a question of Chikara Nakayama. We also give several equivalent conditions defining isogenies of log abelian varieties.

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Heer Zhao. 2019-09-03. Extending finite subgroup schemes of semi-stable abelian varieties via log abelian varieties. https://doi.org/10.1215/21562261-2019-0049

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