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Mathematics of the USSR-Izvestiya, 1990, Volume 34, Issue 1, Pages 121–145
DOI: https://doi.org/10.1070/IM1990v034n01ABEH000610
(Mi im1233)
 

This article is cited in 49 scientific papers (total in 49 papers)

Homology of the full linear group over a local ring, and Milnor's $K$-theory

Yu. P. Nesterenko, A. A. Suslin
References:
Abstract: For rings with a large number of units the authors prove a strengthened theorem on homological stabilization: the homomorphism $H_k(\operatorname{GL}_n(A))\to H_k(\operatorname{GL}(A))$ is surjective for $n\geqslant k+\operatorname{sr}A-1$ and bijective for $n\geqslant k+\operatorname{sr}A$. If $A$ is a local ring with an infinite residue field, then this result admits further refinement: the homomorphism $H_n(\operatorname{GL}_n(A))\to H_n(\operatorname{GL}(A))$ is bijective and the factor group $H_n(\operatorname{GL}(A))/H_n(\operatorname{GL}_{n-1}(A))$ is canonically isomorphic to Milnor's $n$ th $K$-group of the ring $A$. The results are applied to compute the Chow groups of algebraic varieties.
Bibliography: 16 titles.
Received: 02.04.1987
Bibliographic databases:
UDC: 519.4
MSC: 19D45
Language: English
Original paper language: Russian
Citation: Yu. P. Nesterenko, A. A. Suslin, “Homology of the full linear group over a local ring, and Milnor's $K$-theory”, Math. USSR-Izv., 34:1 (1990), 121–145
Citation in format AMSBIB
\Bibitem{NesSus89}
\by Yu.~P.~Nesterenko, A.~A.~Suslin
\paper Homology of the full linear group over a~local ring, and Milnor's $K$-theory
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 1
\pages 121--145
\mathnet{http://mi.mathnet.ru//eng/im1233}
\crossref{https://doi.org/10.1070/IM1990v034n01ABEH000610}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=992981}
\zmath{https://zbmath.org/?q=an:0684.18001|0668.18011}
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  • https://doi.org/10.1070/IM1990v034n01ABEH000610
  • https://www.mathnet.ru/eng/im/v53/i1/p121
  • This publication is cited in the following 49 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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