Clausen, Dustin and Mathew, Akhil and Naumann, Niko and Noel, Justin (2020) Descent in algebraic K-theory and a conjecture of Ausoni-Rognes. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 22 (4). pp. 1149-1200. ISSN 1435-9855,
Full text not available from this repository. (Request a copy)Abstract
Let A -> B be a G-Galois extension of rings, or more generally of E-infinity-ring spectra in the sense of Rognes. A basic question in algebraic K-theory asks how close the map K(A)-> K(B)(hG) is to being an equivalence, i.e., how close algebraic K-theory is to satisfying Galois descent. An elementary argument with the transfer shows that this equivalence is true rationally in most cases of interest. Motivated by the classical descent theorem of Thomason, one also expects such a result after periodic localization. We formulate and prove a general result which enables one to promote rational descent statements as above into descent statements after periodic localization. This reduces the localized descent problem to establishing an elementary condition on K-0(-)circle times Q. As applications, we prove various descent results in the periodically localized K-theory, TC, THH, etc. of structured ring spectra, and verify several cases of a conjecture of Ausoni and Rognes.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SPECTRA; LOCALIZATION; NILPOTENCY; COHOMOLOGY; GENERATORS; FUNCTORS; DUALITY; Algebraic K-theory; descent; Galois extensions; structured ring spectra; chromatic homotopy theory |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Niko Naumann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Apr 2021 09:01 |
| Last Modified: | 07 Apr 2021 09:01 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45496 |
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