On the comparison theorem for étale cohomology of non-Archimedean analytic spaces

Let ϕ:Y →X be a morphism of finite type between schemes of locally finite type over a non-Archimedean fieldk, and letF be an étale constructible sheaf onY. In [Ber2] we proved that if the torsion orders ofF are prime to the characteristic of the residue field ofk then the canonical homomorphisms (R Q ϱ*F)an →R q ϱ * an F an are isomorphisms. In this paper we extend the above result to the class of sheavesF with torsion orders prime to the characteristic ofk.