Research-Some examples and results on integral p-adic Hodge filtrations

Research

Algebra & Combinatorics Seminar

Some examples and results on integral p-adic Hodge filtrations

Speaker: LI Shizhan (University of Michigan)
Time: Dec 24, 2020, 09:30-10:30
Location: Zoom ID: 693 5107 6331 Passcode: sustech123

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 in terms of 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.