Intermediate extensions of perverse constructible ${\mathbb{F}}_p$-sheaves commute with smooth pullbacks

Abstract

We prove that intermediate extensions of perverse constructible ${\mathbb{F}}_p$-sheaves commute with smooth pullbacks for schemes admitting a closed embedding into a smooth scheme over a field of characteristic $p$ (embeddable schemes for short). 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 $f:X\to Y$ of embeddable schemes.

arXiv comment17 pages, v2: added more details for some proofs, reorganized Section 2; v3: final version

References in corpus (2)

• Revêtements étales et groupe fondamental (SGA 1)
• Functorial Test Modules