A new approach to de Rham-Witt complexes, after Bhatt, Lurie, and Mathew
type: Item
instance of: scholarly article
title: A new approach to de Rham-Witt complexes, after Bhatt, Lurie, and Mathew
zbMATH Open document ID: 1490.14031
DOI: 10.4171/RSMUP/86
author: Luc Illusie
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2022-02-14T00:00:00Z
review text: This paper is a report on [\textit{B. Bhatt} et al., Revisiting the de Rham-Witt complex. Paris: Société Mathématique de France (SMF) (2021; Zbl 1478.14038)]. As the author said: ``My aim ... is 4-fold: -- put [loc. cit.] in a broader historical perspective; -- give a short and (as much as possible) self-contained summary of its basic definitions, constructions, and properties; -- discuss examples; -- discuss open questions and perspectives.'' Since this report was written before the final publication of [loc. cit.], a few proofs presented here are different from the published version of [loc. cit.]. These old proofs are sometimes more direct, if slightly less conceptual, than those appeared in the published version.
reviewed by: Dingxin Zhang
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 14G17
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 7473031
zbMATH Keywords: Cartier isomorphism
zbMATH Keywords: crystalline cohomology
zbMATH Keywords: de Rham complex
zbMATH Keywords: de Rham cohomology
zbMATH Keywords: de Rham-Witt complex
zbMATH Keywords: Dieudonné complex
zbMATH Keywords: Frobenius morphism
zbMATH Keywords: Kodaira vanishing
zbMATH Keywords: lifting
zbMATH Keywords: Nygaard filtration
zbMATH Keywords: \(p\)-adic Hodge theory
zbMATH Keywords: rigid cohomology
zbMATH Keywords: seminormal ring
zbMATH Keywords: slope spectral sequence
zbMATH Keywords: toric singularity
zbMATH Keywords: Witt vectors
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/rsmup/86
OpenAlex ID: W4200281063
description: scientific article; zbMATH DE number 7473031