Timeline for On Topological Hochschild Homology
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 7, 2019 at 5:28 | comment | added | Shay Ben Moshe | Lars Hesselholt and Thomas Nikolaus recently uploaded this survey (part of the Handbook on Homotopy Theory), which might be useful for people interested in this question, to the arxiv arxiv.org/abs/1905.08984. | |
| Jun 14, 2018 at 9:21 | comment | added | Leon Hendrian | Thomas Nikolaus has some lecture notes available on his homepage, see uni-muenster.de/IVV5WS/WebHop/user/nikolaus/papers.html . | |
| Jun 4, 2018 at 7:02 | comment | added | Denis Nardin | @aaaaaaaaaaaaaaa Well, computing TC is a little more involved than just taking homotopy fixed points... (although recent results of Nikolaus and Scholze significantly simplified the situation, at least in the bounded below case) | |
| Jun 3, 2018 at 21:28 | comment | added | user124192 | The K-groups completed away from p are computed very quickly from Gabber rigidity; the trouble is the rational part--which you can compute by Goodwillie's thm. and classical cyclic homology--and the p-torsion, which you can (in principle) compute by making a THH calculation and then running the (rather tough) spectral sequences to get from there to TC, then comparing the LES in TC-groups to the LES in K-groups, for the ring map A -> k. This method computes K-groups that nobody seems to be able to compute any other way; try computing the p-torsion in K_*(F_p[x]/x^2) by other means, for example! | |
| Jun 3, 2018 at 21:21 | comment | added | user124192 | Madsen's survey article "Algebraic K-theory and traces" is quite nice, although was written well before the most recent surge of interest in connections between THH and p-adic Hodge theory, so the most recent ideas in that direction won't be found in Madsen's survey. Briefly, and not in the widest possible generality: if A is an Artin local ring with residue field k of char. p, then the fiber of the alg K-thy map K(A) -> K(k) agrees after p-completion with the fiber of the topological cyclic homology map TC(A) -> TC(k). You compute TC by taking htpy fixed-points of a group action on THH. | |
| Jun 3, 2018 at 20:57 | review | First posts | |||
| Jun 3, 2018 at 21:07 | |||||
| Jun 3, 2018 at 20:55 | history | asked | user125208 | CC BY-SA 4.0 |