Over a regular base with a normal crossings divisor, the p-divisible group (and n-torsion) of a degenerating abelian scheme extends uniquely to a log p-divisible group (log finite group scheme).
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Log $p$-divisible groups associated with semi-abelian degeneration
Over a regular base with a normal crossings divisor, the p-divisible group (and n-torsion) of a degenerating abelian scheme extends uniquely to a log p-divisible group (log finite group scheme).