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Completed prismatic F-crystals and crystalline Zp-local systems
- Part of
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- Journal:
- Compositio Mathematica / Volume 160 / Issue 5 / May 2024
- Published online by Cambridge University Press:
- 18 April 2024, pp. 1101-1166
- Print publication:
- May 2024
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- Article
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We introduce the notion of completed
$F$-crystals on the absolute prismatic site of a smooth 
$p$-adic formal scheme. We define a functor from the category of completed prismatic 
$F$-crystals to that of crystalline étale 
$\mathbf {Z}_p$-local systems on the generic fiber of the formal scheme and show that it gives an equivalence of categories. This generalizes the work of Bhatt and Scholze, which treats the case of a mixed characteristic complete discrete valuation ring with perfect residue field.
