Relative $(\varphi,Γ)$-modules and prismatic $F$-crystals (2110.06076v2)

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 \'etale $\mathbb Z_p$-local systems on the generic fiber of $\mathfrak X$. We also compare the cohomology of the corresponding coefficients.