Relative $(\ddot{I}†,\hat{I}“)$-modules and prismatic $F$-crystals

Abstract

In this paper, we prove that for any $p$-adic smooth separated formal scheme $\mathfrak{X}$, the category of prismatic $F$-crystals with $I$ inverted is equivalent to the category of étale ${\mathbb{Z}}_p$-local systems on the generic fiber of $\mathfrak{X}$. We also compare the cohomology of the corresponding coefficients.

Minor mistakes corrected