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Logarithmic Prismatic Cohomology I

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arxiv 2007.14037 v3 pith:KNDZNXYT submitted 2020-07-28 math.AG math.NT

Teruhisa Koshikawa This is my paper · ORCID
classification math.AGmath.NT
keywords logarithmiccohomologydeltaprismaticringsbhattbreuil-kisincall
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Potential semistability of Finite height Galois representations: Relative case

    math.NT 2026-06 unverdicted novelty 7.0 of 10

    Defines finite height for étale Z_p-local systems on adic spaces over p-adic fields and proves potential semistability after finite étale cover via analytic prismatic F-crystals and external purity results.

  2. A prismatic-etale comparison theorem in the semistable case

    math.AG 2025-07 conditional novelty 7.0 of 10

    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...

  3. A motivic approach to rational $p$-adic cohomologies

    math.AG 2025-08 conditional novelty 4.0 of 10

    Smooth complete intersections in projective toric varieties over p-adic fields satisfy the p-adic weight-monodromy conjecture, here re-proven through motivic nearby cycles and a monodromy-category equivalence.

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