Arbeitsgemeinschaft: Topological Cyclic Homology
Lars Hesselholt
University of Copenhagen, Denmark and Nagoya University, JapanPeter Scholze
Universität Bonn, Germany
Abstract
Introduced by Bökstedt–Hsiang–Madsen in the nineties, topological cyclic homology is a manifestation of the dual visions of Connes–Tsygan and Waldhausen to extend de Rham cohomology to a noncommutative setting and to replace algebra by higher algebra. The cohomology theory that ensues receives a denominator-free Chern character from algebraic -theory, used by Hesselholt–Madsen to evaluate the -adic -theory of -adic fields. More recently, Bhatt–Morrow–Scholze have defined a “motivic” filtration of topological cyclic homology and its variants, the filtration quotients of which give rise to their denominator-free -adic Hodge theory .
Cite this article
Lars Hesselholt, Peter Scholze, Arbeitsgemeinschaft: Topological Cyclic Homology. Oberwolfach Rep. 15 (2018), no. 2, pp. 805–940
DOI 10.4171/OWR/2018/15