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arXiv · 2107.12240

A prismatic approach to $(φ, \hat G)$-modules and $F$-crystals

Heng Du·Tong Liu
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Abstract

We give a new construction of $(φ, \hat G)$-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 $\mathcal{O}_Δ$-modules over $(\mathcal{O}_K)_Δ$ and the category of lattices in crystalline representations of $G_K$, 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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Heng Du, Tong Liu. 2023-07-31. A prismatic approach to $(φ, \hat G)$-modules and $F$-crystals. https://arxiv.org/abs/2107.12240

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