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学术科研

Algebra & Combinatorics Seminar

Some examples and results on integral p-adic Hodge filtrations

演讲者：李时璋（密歇根大学）
时间：2020-12-24 09:30-10:30
地点：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.