On the periodic topological cyclic homology of DG categories in characteristic p

Abstract

We prove that the $p$-adically completed periodic topological cyclic homology of a DG category over a perfect field $k$ of characteristic $p>2$ is isomorphic to the ($p$-adically completed) periodic cyclic homology of a lifting of the DG category over the Witt vectors $W(k)$.

20 pages. A new section on the crystalline periodic cyclic homology of smooth schemes is added

References in corpus (3)

• p-adic derived de Rham cohomology
• On the Blumberg-Mandell Künneth theorem for TP
• Kaledin's degeneration theorem and topological Hochschild homology