Abstract
Using topological cyclic homology, we give a refinement of Beilinson’s p-adic Goodwillie isomorphism between relative continuous K-theory and cyclic homology. As a result, we generalize results of Bloch–Esnault–Kerz and Beilinson on the p-adic deformations of K-theory classes. Furthermore, we prove structural results for the Bhatt–Morrow–Scholze filtration on TC and identify the graded pieces with the syntomic cohomology of Fontaine–Messing.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3707-3806 |
| Number of pages | 100 |
| Journal | Duke Mathematical Journal |
| Volume | 171 |
| Issue number | 18 |
| DOIs | |
| State | Published - Dec 1 2022 |
Funding
We are very grateful to Peter Scholze for suggesting this question to us and for sharing many insights. We would also like to thank Johannes Ansch\u00FCtz, Alexander Beilinson, Bhargav Bhatt, H\u00E9l\u00E8ne Esnault, Lars Hesselholt, Luc Illusie, Moritz Kerz, Arthur-C\u00E9sar Le Bras, Wies\u0142awa Nizio\u0142, and Sam Raskin for helpful conversations. The third author would like to thank Uwe Jannsen, Moritz Kerz, and Guido Kings for organizing and inviting him to the 2014 Kleinwalsertal workshop on Beilinson\u2019s paper [8]. Two referees provided detailed, invaluable comments on the paper which has been improved as a result. The first two authors would like to thank the University of Bonn and the University of M\u00FCnster for their hospitality. This material is based upon work supported by National Science Foundation (NSF) grant DMS-1440140 while the first three authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the spring 2019 semester. The first author was supported by NSF grant DMS-1552766. This work was done while the second author was a Clay Research Fellow. The fourth author was funded by the Deutsche Forschungsgemeinschaft under Germany\u2019s Excellence Strategy EXC 2044-390685587, Mathematics M\u00FCnster: Dynamics\u2013Geometry\u2013Structure. The first two authors would like to thank the University of Bonn and the University of M\u00FCnster for their hospitality. This material is based upon work supported by National Science Foundation (NSF) grant DMS-1440140 while the first three authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the spring 2019 semester. The first author was supported by NSF grant DMS-1552766. This work was done while the second author was a Clay Research Fellow. The fourth author was funded by the Deutsche Forschungsgemein-schaft under Germany\u2019s Excellence Strategy EXC 2044-390685587, Mathematics M\u00FCnster: Dynamics\u2013Geometry\u2013Structure.
ASJC Scopus subject areas
- General Mathematics