Prismatic $F$-crystals and crystalline Galois representations

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.

arXiv commentv2: small updates