Extending finite subgroup schemes of semi-stable abelian varieties via log abelian varieties
arXiv:1909.01038 · doi:10.1215/21562261-2019-0049
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.
arXiv commentto appear in Kyoto Journal of Mathematics