Yanik Kleibrink (Darmstadt): Period Maps from Log Prismatic Realization Functors

I will start by surveying the recent development of logarithmic prismatic cohomology by Koshikawa and Yao that extends the original work by Bhatt and Scholze. In particular, I will introduce the logarithmic prismatic realization functor for toroidal compactifications of integral canonical models of Shimura varieties of Hodge type constructed by Inoue, which extends the realization functor of Imai, Kato, and Youcis. Using this realization functor, I will present work-in-progress concerning the definition of a mod \(p\)-period map of the special fiber of an integral canonical model of Shimura variety of Hodge type to the stack of \(G\Zip\)s. Ideally, this construction coincides with an existing construction by Goldring and Koskivirta and enables the usage of prismatic methods in the study of Ekedahl-Oort strata.

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