Intermediate extensions of perverse constructible [formula omitted]-sheaves commute with smooth pullbacks

Abstract

We prove that intermediate extensions of perverse constructible Fp-sheaves commute with smooth pullbacks for embeddable schemes over a field of characteristic p. Along the way we also prove that the equivalence of categories of Cartier crystals with unit R[F]-modules commutes with f! for a smooth morphism f:X→Y of embeddable schemes.