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

TL;DR

This paper proves that intermediate extensions of perverse constructible $ ext{F}_p$-sheaves and the equivalence of certain categories commute with smooth pullbacks on embeddable schemes in characteristic $p$, advancing understanding in algebraic geometry.

Contribution

It establishes the commutation of intermediate extensions and category equivalences with smooth pullbacks for embeddable schemes in characteristic $p$, providing new tools for algebraic geometry in positive characteristic.

Findings

Intermediate extensions commute with smooth pullbacks on embeddable schemes.

Equivalence of Cartier crystals with $R[F]$-modules commutes with $f^!$ for smooth morphisms.

Results apply to schemes admitting a closed embedding into smooth schemes over a field of characteristic $p$.

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.