Some examples and results on integral p-adic Hodge filtrations

Abstract: Given a smooth proper scheme over a mixed characteristic DVR, we try to understand to what extent the special fiber knows the Hodge numbers of the generic fiber. I'll provide some examples as well as a theorem showing that in "good" situations some numbers defined purely using the special fiber actually give the Hodge numbers of the generic fiber. This naturally leads to consideration of Breuil-Kisin prismatic cohomology, and I'll describe an example which illustrates certain pathological behavior of Hodge-Tate and Hodge-de Rham spectral sequences in mixed characteristic situations.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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