Some recent advances in topological Hochschild homology

Abstract

We give an account of the construction of the Bhatt--Morrow--Scholze motivic filtration on topological cyclic homology and related invariants, focusing on the case of equal characteristic $p$ and the connections to crystalline and de Rham--Witt theory.

39 pages, survey paper; minor corrections

References in corpus (3)

• Higher Topos Theory
• Tensor triangular geometry of filtered objects and sheaves
• Revisiting derived crystalline cohomology

Cited by in corpus (2)

• Syntomic complexes and $p$-adic étale Tate twists
• Floor, ceiling, slopes, and $K$-theory