Log Prismatic Dieudonné theory and its application to Shimura varieties

We study the log version of the prismatic Dieudonné theory established by Anschütz-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.