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).
Log Prismatic Dieudonn\'{e} theory and its application to Shimura varieties
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abstract
We study the log version of the prismatic Dieudonn\'{e} theory established by Ansch\"{u}tz-Le Bras. By applying this result to the integral toroidal compactification of a Shimura variety of Hodge type, we extend the prismatic realization, originally constructed by Imai-Kato-Youcis, to the compactification. This extension enables us to prove Lovering's conjecture on $p$-adic comparison isomorphisms for Shimura varieties.
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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).