Logarithmic de Rham--Witt complexes via the Décalage operator

2018/08/28 by Yao, Zijian
#14F40 #14G22 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14F30 #Secondary 14G20

paper · doi:10.48550/arxiv.1808.09120

Abstract

We provide a new formalism of de Rham--Witt complexes in the logarithmic setting. This construction generalizes 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 apply our formalism to obtain a more direct proof of the log crystalline comparison of A_inf-cohomology in the case of semistable reduction, which is established by Cesnavicius--Koshiwara.

Related

• Logarithmic De Rham, Infinitesimal and Betti Cohomologies
• On comparison between relative log de Rham-Witt cohomology and relative log crystalline cohomology
• Logarithmic Crystalline Representations
• Logarithmic A_{\rm inf}-cohomology
• Logarithmic Comparison Theorems