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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Depth and detection for Noetherian unstable algebras
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by Drew Heard PDF
Trans. Amer. Math. Soc. 373 (2020), 7429-7454 Request permission

Abstract:

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.
References
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Additional Information
  • Drew Heard
  • Affiliation: Fakultät für Mathematik, Universität Regensburg, 93053 Regensburg, Germany
  • Address at time of publication: Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
  • MR Author ID: 1112422
  • ORCID: 0000-0002-0895-3354
  • Email: drew.k.heard@ntnu.no
  • Received by editor(s): July 23, 2019
  • Received by editor(s) in revised form: March 18, 2020
  • Published electronically: August 5, 2020
  • Additional Notes: This work was supported by SFB 1085 “Higher Invariants” (Universität Regensburg), funded by the Deutsche Forschungsgemeinschaft.
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 7429-7454
  • MSC (2010): Primary 55S10, 13C15, 57T05
  • DOI: https://doi.org/10.1090/tran/8157
  • MathSciNet review: 4155212