Prismatic $F$-crystals and crystalline Galois representations

TL;DR

This paper establishes an equivalence between prismatic F-crystals on the ring of integers of a p-adic field and lattices in crystalline Galois representations, advancing the understanding of p-adic Hodge theory.

Contribution

It proves the categorical equivalence between prismatic F-crystals and lattices in crystalline Galois representations, providing a new framework for studying p-adic Hodge structures.

Findings

Category of prismatic F-crystals is equivalent to lattices in crystalline Galois representations

Provides a new perspective linking prismatic cohomology and Galois representations

Advances the theoretical foundation of p-adic Hodge theory

Abstract

Let $K$ be a complete discretely valued field of mixed characteristic $(0,p)$ with perfect residue field. We prove that the category of prismatic $F$-crystals on $\mathcal O_K$ is equivalent to the category of lattices in crystalline $G_K$-representations.