A prismatic approach to (φ,Ĝ )-modules and F-crystals

Heng Du YMSC, Tsinghua Tong Liu Purdue University

Number Theory Algebraic Geometry mathscidoc:2205.24003

We give a new construction of (φ,Ĝ )-modules using the theory of prisms developed by Bhatt and Scholze. As an application, we give a new proof about the equivalence between the category of prismatic F-crystals in finite locally free Δ-modules over (K)Δ and the category of lattices in crystalline representations of GK, where K is a complete discretely valued field of mixed characteristic with perfect residue field. We also generalize this result to semi-stable representations using the absolute logarithmic prismatic site defined by Koshikawa.
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@inproceedings{henga,
  title={A prismatic approach to (φ,Ĝ )-modules and F-crystals},
  author={Heng Du, and Tong Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517153729657131233},
}
Heng Du, and Tong Liu. A prismatic approach to (φ,Ĝ )-modules and F-crystals. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517153729657131233.
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