Integral \(p\)-adic Hodge filtrations in low dimension and ramification
type: Item
instance of: scholarly article
title: Integral \(p\)-adic Hodge filtrations in low dimension and ramification
DOI: 10.4171/JEMS/1237
author: Shizhang Li
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2022-10-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/2002.00431
review text: Summary: Given an integral \(p\)-adic variety, we observe that if the integral Hodge-de Rham spectral sequence behaves nicely, then the special fiber knows the Hodge numbers of the generic fiber. Applying recent advancements of integral \(p\)-adic Hodge theory, we show that such a nice behavior is guaranteed if the \(p\)-adic variety can be lifted to an analogue of second Witt vectors and satisfies some bound on dimension and ramification index. This is a (ramified) mixed characteristic analogue of results due to Deligne-Illusie, Fontaine-Messing, and Kato. Lastly, we discuss an example illustrating the necessity of the aforementioned lifting condition, which is of independent interest.
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 14G22
zbMATH DE Number: 7608242
zbMATH Keywords: de Rham cohomology
zbMATH Keywords: prismatic cohomology
zbMATH Keywords: \(p\)-adic Hodge theory
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7608242