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Journal of the Institute of Mathematics of Jussieu (1)

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LOGARITHMIC DE RHAM–WITT COMPLEXES VIA THE DÉCALAGE OPERATOR
Part of
- (Co)homology theory
- Arithmetic problems. Diophantine geometry
Zijian Yao
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 3 / May 2023

Published online by Cambridge University Press:

26 August 2021, pp. 1319-1382

Print publication:

May 2023
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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.