Completed prismatic F-crystals and crystalline Zp-local systems

Heng Du YMSC, Tsinghua Tong Liu Purdue University Yong Suk Moon University of Arizona Koji Shimizu Berkeley University

Number Theory Algebraic Geometry mathscidoc:2205.24004

2022.3
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 ├ętale Zp-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 complete discrete valuation ring with perfect residue field.
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@inproceedings{heng2022completed,
  title={Completed prismatic F-crystals and crystalline Zp-local systems},
  author={Heng Du, Tong Liu, Yong Suk Moon, and Koji Shimizu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517153956962847234},
  year={2022},
}
Heng Du, Tong Liu, Yong Suk Moon, and Koji Shimizu. Completed prismatic F-crystals and crystalline Zp-local systems. 2022. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517153956962847234.
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