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arXiv · 2110.06076

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

Yu Min·Yupeng Wang
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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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Yu Min, Yupeng Wang. 2021-10-12. Relative $(\varphi,\Gamma)$-modules and prismatic $F$-crystals. https://arxiv.org/abs/2110.06076

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