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LOGARITHMIC DE RHAM–WITT COMPLEXES VIA THE DÉCALAGE OPERATOR

Part of: (Co)homology theory Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  26 August 2021

Zijian Yao Open the ORCID record for Zijian Yao [Opens in a new window]
Zijian Yao*
Affiliation:
Department of Mathematics, Harvard University
*
zijian.yao.math@gmail.com
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Abstract

We provide a new formalism of de Rham–Witt complexes in the logarithmic setting. This construction generalises a result of Bhatt–Lurie–Mathew and agrees with those of Hyodo–Kato and Matsuue for log-smooth schemes of log-Cartier type. We then use our construction to study the monodromy action and slopes of Frobenius on log crystalline cohomology.

Keywords

de Rham-Witt complexlog crystalline cohomologymonodromy operatorde Rham cohomologyNygaard filtrationslopes of Frobenius

MSC classification

Primary: 14F30: $p$-adic cohomology, crystalline cohomology
Secondary: 14G20: Local ground fields 14G22: Rigid analytic geometry 14F40: de Rham cohomology
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 3 , May 2023 , pp. 1319 - 1382
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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