Logarithmic Prismatic Cohomology I

Abstract

We introduce a logarithmic variant of the notion of $\delta$-rings, which we call ${\delta }_{\log }$-rings, and use it to define a logarithmic version of the prismatic site introduced by Bhatt and Scholze. In particular, this enables us to construct the Breuil-Kisin cohomology in the semistable case.

64 pages, preliminary version

Cited by in corpus (5)

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• Essential dimension via prismatic cohomology
• Formality of little disks and algebraic geometry
• Crystalline condition for $A_{\inf }$-cohomology and ramification bounds
• A prismatic approach to $(\phi ,\hat{G})$-modules and $F$-crystals