Land, Markus and Tamme, Georg (2019) On the K-theory of pullbacks. ANNALS OF MATHEMATICS, 190 (3). pp. 877-930. ISSN 0003-486X, 1939-8980
Full text not available from this repository.Abstract
To any pullback square of ring spectra we associate a new ring spectrum and use it to describe the failure of excision in algebraic K-theory. The construction of this new ring spectrum is categorical and hence allows us to determine the failure of excision for any localizing invariant in place of K-theory. As immediate consequences we obtain an improved version of Suslin's excision result in K-theory, generalizations of results of Geisser and Hessel-holt on torsion in (bi)relative K-groups, and a generalized version of pro-excision for K-theory. Furthermore, we show that any truncating invariant satisfies excision, nilinvariance, and cdh-descent. Examples of truncating invariants include the fibre of the cyclotomic trace, the fibre of the rational Goodwillie-Jones Chern character, periodic cyclic homology in characteristic zero, and homotopy K-theory. Various of the results we obtain have been known previously, though most of them in weaker forms and with less direct proofs.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CYCLIC HOMOLOGY; A(1)-HOMOTOPY THEORY; EXCISION; LOCALIZATION; DESCENT; K-theory; birelative K-theory; localizing invariant; excision; cdh-descent |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Ulrich Bunke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 Mar 2020 10:55 |
| Last Modified: | 25 Mar 2020 10:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/25933 |
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