Logarithmic Prismatic Cohomology I

We introduce a logarithmic variant of the notion of $δ$-rings, which we call $δ_{\log}$-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.

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