Cambridge Journal of Mathematics

Volume 11 (2023)

Number 2

Prismatic $F$-crystals and crystalline Galois representations

Pages: 507 – 562



Bhargav Bhatt (University of Michigan, Ann Arbor, Mich., U.S.A.; and IAS & Princeton University, Princeton, New Jersey, U.S.A.)

Peter Scholze (Max Planck Institut für Mathematik, Bonn, Germany)


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.

Received 4 July 2021

Published 6 June 2023