Cartier modules and cyclotomic spectra

Abstract

We construct and study a t t -structure on p p -typical cyclotomic spectra and explain how to recover crystalline cohomology of smooth schemes over perfect fields using this t t -structure. Our main tool is a new approach to p p -typical cyclotomic spectra via objects we call p p -typical topological Cartier modules. Using these, we prove that the heart of the cyclotomic t t -structure is the full subcategory of derived V V -complete objects in the abelian category of p p -typical Cartier modules.