Log Abelian Varieties over a Log Point

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.

2010 Mathematics Subject Classification: Primary 14D06; Secondary 14K99, 11G99.

Keywords and Phrases: log abelian varieties with constant degeneration, endomorphism algebras, Poincaré complete reducibility theorem, dual short exact sequence for isogenies.

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