Prismatic F ‐crystals and Wach modules

We show that the category of analytic/completed prismatic on the absolute prismatic site of a small (unramified at ) base ring is naturally equivalent to the category of relative Wach modules from the theory of . The result is obtained by showing that the data of the Galois action on a Wach module is equivalent to the data of a prismatic stratification on the underlying . Along the way, we obtain new descent results for relative Wach modules.