Fourier--Mukai transforms commuting with Frobenius

Abstract

We show that a Fourier--Mukai equivalence between smooth projective varieties of characteristic $p$ which commutes with either pushforward or pullback along Frobenius is a composition of shifts, isomorphisms, and tensor product with invertible sheaves whose $(p-1)$th tensor power is trivial.

arXiv commentFinal version. To appear in the Bulletin of the London Mathematical Society