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A stability property for linear groups


Author: Marian F. Anton
Journal: Proc. Amer. Math. Soc. 134 (2006), 93-98
MSC (2000): Primary 19D55, 20G30
DOI: https://doi.org/10.1090/S0002-9939-05-07946-3
Published electronically: June 14, 2005
MathSciNet review: 2170547
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Abstract | References | Similar Articles | Additional Information

Abstract: For suitable rings of integers $R$, we show that the mod $p$ group cohomology for $GL_{n+3p-5}(R)$ comes from $GL_\infty(R)$ when restricted to the diagonal matrices $D_n(R)$ for all ranks $n\ge 2$.


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  • 1. Marian F. Anton, On a conjecture of Quillen at the prime $3$, J. Pure Appl. Algebra 144 (1999), 1-20. MR 2000m:19003
  • 2. -, An elementary invariant problem and general linear group cohomology restricted to the diagonal subgroup, Trans. Amer. Math. Soc. 355 (2003), 2327-2340 (electronic). MR 2004c:57061
  • 3. Kenneth S. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York, 1994. MR 96a:20072
  • 4. William G. Dwyer, and Eric M. Friedlander, Algebraic and etale $K$-theory, Trans. Amer. Math. Soc. 292 (1985), 247-280. MR 87h:18013
  • 5. W. G. Dwyer and E. M. Friedlander, Conjectural calculations of general linear group homology, Applications of Algebraic $K$-theory to Algebraic Geometry and Number Theory, Part I, II (Boulder, Colo., 1983), Contemp. Math., vol 55, Amer. Math. Soc., Providence, RI, 1986, 135-147. MR 88f:18013
  • 6. William G. Dwyer and Eric M. Friedlander, Topological models for arithmetic, Topology 33 (1994), 1-24. MR 95h:19004
  • 7. Allen Hatcher, Algebraic topology, Cambridge University Press, Cambridge, 2002. MR 2002k:55001
  • 8. Wilberd van der Kallen, Homology stability for linear groups, Invent. Math. 60 (1980), 269-295. MR 82c:18011
  • 9. Stephen A. Mitchell, On the plus construction for $B{\rm GL}\,{\bf Z}[\frac12]$ at the prime $2$, Math. Z. 209 (1992), 205-222. MR 93b:55021
  • 10. -, Units and general linear group cohomology for a ring of algebraic integers, Math. Z. 228 (1998), 207-220. MR 99k:19002
  • 11. Daniel Quillen, The spectrum of an equivariant cohomology ring. I, II, Ann. of Math. (2) 94 (1971), 549-572; ibid. (2) 94 (1971), 573-602. MR 45:7743

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Additional Information

Marian F. Anton
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027 – and – I.M.A.R., P.O. Box 1-764, Bucharest, Romania 70700
Email: anton@ms.uky.edu

DOI: https://doi.org/10.1090/S0002-9939-05-07946-3
Received by editor(s): September 3, 2004
Received by editor(s) in revised form: September 15, 2004
Published electronically: June 14, 2005
Communicated by: Paul Goerss
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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