Cartier modules and cyclotomic spectra

摘要

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.