Geodesic
Log Abelian Varieties over a Log Point
Documenta mathematica, Tome 22 (2017), pp. 505-550
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We study (weak) log abelian varieties with constant degeneration in the log flat topology. If the base is a log point, we further study the endomorphism algebras of log abelian varieties. In particular, we prove the dual short exact sequence for isogenies, Poincaré complete reducibility theorem for log abelian varieties, and the semi-simplicity of the endomorphism algebras of log abelian varieties.
DOI : 10.4171/dm/572
Classification : 11G99, 14D06, 14K99
Mots-clés : log abelian varieties with constant degeneration, Poincaré complete reducibility theorem, dual short exact sequence for isogenies 
@article{10_4171_dm_572,
     author = {Heer Zhao},
     title = {Log {Abelian} {Varieties} over a {Log} {Point}},
     journal = {Documenta mathematica},
     pages = {505--550},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/572},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/572/}
}
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Heer Zhao. Log Abelian Varieties over a Log Point. Documenta mathematica, Tome 22 (2017), pp. 505-550. doi: 10.4171/dm/572

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