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arXiv · 2301.12392

Prismatization over $\mathbf{Z}$

Lance Gurney
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Abstract

The aim of this article is to given an extension of the prismatization functor for $p$-adic formal schemes (whose construction was first sketched by Drinfeld and then given by Bhatt-Lurie) to all schemes over $\mathrm{Spec}(\mathbf{Z})$. We then prove some basic properties of this extension (algebraicity, flatness for syntomic morphisms, perfectness of cohomology) and show that for smooth schemes over $\mathbf{Q}$ this construction recovers (a version of) the filtered de Rham stack.

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Lance Gurney. 2023-01-29. Prismatization over $\mathbf{Z}$. https://arxiv.org/abs/2301.12392

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