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