Heard, Drew (2020) DEPTH AND DETECTION FOR NOETHERIAN UNSTABLE ALGEBRAS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 373 (10). pp. 7429-7454. ISSN 0002-9947, 1088-6850
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For a connected Noetherian unstable algebra R over the mod p Steenrod algebra, we prove versions of theorems of Duflot and Carlson on the depth of R, originally proved when R is the mod p cohomology ring of a finite group. This recovers the aforementioned results, and also proves versions of them when R is the mod p cohomology ring of a compact Lie group, a profinite group with Noetherian cohomology, a Kac-Moody group, a discrete group of finite virtual cohomological dimension, as well as for certain other discrete groups. More generally, our results apply to certain finitely generated unstable R-modules. Moreover, we explain the results in the case of the p-local compact groups of Broto, Levi, and Oliver, as well as in the modular invariant theory of finite groups.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ABELIAN P-SUBGROUPS; CLASSIFYING-SPACES; HOMOTOPY-THEORY; FUSION SYSTEMS; LIE-GROUPS; T-FUNCTOR; COHOMOLOGY; UNIQUENESS; MODULES; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Mar 2021 05:10 |
| Last Modified: | 15 Mar 2021 05:10 |
| URI: | https://pred.uni-regensburg.de/id/eprint/43669 |
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