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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An elementary invariant problem and general linear group cohomology restricted to the diagonal subgroup


Author: Marian F. Anton
Journal: Trans. Amer. Math. Soc. 355 (2003), 2327-2340
MSC (2000): Primary 57T10, 20J05; Secondary 19D06, 55R40
Published electronically: January 27, 2003
MathSciNet review: 1973992
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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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03255-0
PII: S 0002-9947(03)03255-0
Keywords: Etale model, linear group, cohomology, invariants
Received by editor(s): May 1, 2002
Received by editor(s) in revised form: November 14, 2002
Published electronically: January 27, 2003
Article copyright: © Copyright 2003 American Mathematical Society