Number TheoryAlgebraic Geometrymathscidoc: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.
@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.