Prismatic F-crystals and Wach modules

We show a direct equivalence between the category of analytic/completed prismatic F-crystals on the absolute prismatic site of a small (unramified at p) base ring and the category of relative Wach modules from the theory of (, ) -modules. 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 -module.