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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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An elementary invariant problem and general linear group cohomology restricted to the diagonal subgroup
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by Marian F. Anton
Trans. Amer. Math. Soc. 355 (2003), 2327-2340
DOI: https://doi.org/10.1090/S0002-9947-03-03255-0
Published electronically: January 27, 2003

Abstract:

Conjecturally, for $p$ an odd prime and $R$ a certain ring of $p$-integers, the stable general linear group $GL(R)$ and the étale model for its classifying space have isomorphic mod $p$ cohomology rings. In particular, these two cohomology rings should have the same image with respect to the restriction map to the diagonal subgroup. We show that a strong unstable version of this last property holds for any rank if $p$ is regular and certain homology classes for $SL_2(R)$ vanish. We check that this criterion is satisfied for $p=3$ as evidence for the conjecture.
References
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Bibliographic Information
  • Marian F. Anton
  • Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom and IMAR, P.O. Box 1-764, Bucharest, Romania 70700
  • Address at time of publication: Department of Mathematics, University of Kentucky, 715 POT, Lexington, Kentucky 40506-0027
  • Email: Marian.Anton@imar.ro
  • Received by editor(s): May 1, 2002
  • Received by editor(s) in revised form: November 14, 2002
  • Published electronically: January 27, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 2327-2340
  • MSC (2000): Primary 57T10, 20J05; Secondary 19D06, 55R40
  • DOI: https://doi.org/10.1090/S0002-9947-03-03255-0
  • MathSciNet review: 1973992