The prismatization of $p$-adic formal schemes

Bhargav Bhatt; Jacob Lurie

The prismatization of $p$-adic formal schemes

Algebraic Geometry 2022-01-19 v1 Number Theory

Authors: Bhargav Bhatt , Jacob Lurie

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.

Keywords

p-adic formal schemes cartier-witt stack prismatic crystals quasicoherent sheaves cohomology

Cite

@article{arxiv.2201.06124,
  title  = {The prismatization of $p$-adic formal schemes},
  author = {Bhargav Bhatt and Jacob Lurie},
  journal= {arXiv preprint arXiv:2201.06124},
  year   = {2022}
}

Comments

preliminary version, 52 pages, comments welcome

The prismatization of $p$-adic formal schemes

Abstract

Keywords

Cite

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