Mathew, Akhil and Naumann, Niko and Noel, Justin (2017) Nilpotence and descent in equivariant stable homotopy theory. ADVANCES IN MATHEMATICS, 305. pp. 994-1084. ISSN 0001-8708, 1090-2082
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Let G be a finite group and let F be a family of subgroups of G. We introduce a class of G-equivariant spectra that we call F-nilpotent. This definition fits into the general theory of torsion, complete, and nilpotent objects in a symmetric monoidal stable infinity-category, with which we begin. We then develop some of the basic properties of F-nilpotent G-spectra, which are explored further in the sequel to this paper. In the rest of the paper, we prove several general structure theorems for infinity-categories of module spectra over objects such as equivariant real and complex K-theory and Borelequivariant MU. Using these structure theorems and a technique with the flag variety dating back to Quillen, we then show that large classes of equivariant cohomology theories for which a type of complex-orientability holds are nilpotent for the family of abelian subgroups. In particular, we prove that equivariant real and complex K-theory, as well as the Borel-equivariant versions of complex-oriented theories, have this property. (C)2016 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MOORE SPECTRAL SEQUENCE; K-THEORY; ELLIPTIC-OPERATORS; COHOMOLOGY; CATEGORIES; SUBGROUPS; HOMOLOGY; MODULES; INDEX; MODEL; Stable equivariant homotopy theory; Stable homotopy theory; Localization; Completion; Nilpotence; Koszul duality; Eilenberg-Moore spectral sequence; Infinity categories; Tensor triangulated categories; Spectral sequences; Descent; Unipotence; Equivariant topological K-theory |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Niko Naumann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:01 |
| Last Modified: | 19 Feb 2019 10:14 |
| URI: | https://pred.uni-regensburg.de/id/eprint/562 |
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