Log $p$-divisible groups associated with semi-abelian degeneration

Abstract

In this paper, we prove that, when an abelian scheme has semi-abelian degeneration along normal crossings divisor in a regular base scheme, a finite flat group scheme of torsion points of the abelian scheme degenerates to a log finite group scheme, which captures more information than a quasi-finite flat group scheme of torsion points of the semi-abelian scheme.