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Logarithmic prismatic cohomology II
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abstract
We continue to study the logarithmic prismatic cohomology defined by the first author, and complete the proof of the de Rham comparison and \'etale comparison generalizing those of Bhatt and Scholze. We prove these comparisons for a derived version of logarithmic prismatic cohomology, and, along the way, we construct a suitable Nygaard filtration and explain a relation between $F$-crystals and $\mathbb{Z}_p$-local systems in the logarithmic setting.
Forward citations
Cited by 2 Pith papers
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Prismatic cohomology and $A_{\inf}$-cohomology with coefficients
Prismatic cohomology of a locally finite free prismatic crystal is canonically isomorphic to A_inf-cohomology of the associated relative Breuil-Kisin-Fargues module, for smooth p-adic formal schemes over the ring of i...
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A prismatic-etale comparison theorem in the semistable case
Breuil-Kisin cohomology of analytic log prismatic F-crystals on semistable p-adic formal schemes is canonically isomorphic, after tensoring with A_inf and inverting mu, to the etale cohomology of the corresponding sem...
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