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arXiv · 2201.06124

The prismatization of $p$-adic formal schemes

Bhargav Bhatt·Jacob Lurie
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Abstract

In this note, we introduce and study the Cartier--Witt stack $\mathrm{WCart}_X$ attached to a $p$-adic formal scheme $X$ as well as some variants. In particular, we reinterpret the notion of prismatic crystals on $X$ and their cohomology in terms of quasicoherent sheaf theory on $\mathrm{WCart}_X$ in favorable situations.

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Bhargav Bhatt, Jacob Lurie. 2022-01-16. The prismatization of $p$-adic formal schemes. https://arxiv.org/abs/2201.06124

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