Relative $(\varphi,\Gamma)$-modules and prismatic $F$-crystals

Yu Min; Yupeng Wang

Relative $(\varphi,\Gamma)$-modules and prismatic $F$-crystals

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arxiv 2110.06076 v2 pith:KNP6XUUW submitted 2021-10-12 math.AG math.NT

Yu Min , Yupeng Wang This is my paper · ORCID

classification math.AGmath.NT

keywords categorycrystalsmathfrakprismaticadiccoefficientscohomologycompare

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abstract

In this paper, we prove that for any $p$-adic smooth separated formal scheme $\mathfrak X$, the category of prismatic $F$-crystals with $I$ inverted is equivalent to the category of \'etale $\mathbb Z_p$-local systems on the generic fiber of $\mathfrak X$. We also compare the cohomology of the corresponding coefficients.

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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...

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