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Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 114, Pages 187–195 (Mi znsl1778)  

This article is cited in 12 scientific papers (total in 12 papers)

Cancellation over affine varieties

A. A. Suslin
Abstract: It is proved that if $X$ is a smooth affine curve over a field $F$ of characteristic $\ne\ell$, then the group $SK_1(X)/\ell SK_1(X)$ is isomorphic to a subgroup of the йtale cohomology group $H^3_{et}(X,\mu_e^{\otimes2})$ and if $F$ is algebraically closed, then $SK_1(X)$ is a uniquely divisible group. The following cancellation theorem is obtained from results about $SK_1$ for curves: If $X$ is a normal affine variety of dimension $n$ over a field $F$, and if $\operatorname{char}F>n$ and $c.d._\ell(F)\leqslant1$ for any prime $\ell\leqslant n$ then any stably trivial vector bundle of rank $n$ over $X$ is trivial.
English version:
Journal of Soviet Mathematics, 1984, Volume 27, Issue 4, Pages 2974–2980
DOI: https://doi.org/10.1007/BF01410752
Bibliographic databases:
UDC: 519.46
Language: Russian
Citation: A. A. Suslin, “Cancellation over affine varieties”, Modules and algebraic groups, Zap. Nauchn. Sem. LOMI, 114, "Nauka", Leningrad. Otdel., Leningrad, 1982, 187–195; J. Soviet Math., 27:4 (1984), 2974–2980
Citation in format AMSBIB
\Bibitem{Sus82}
\by A.~A.~Suslin
\paper Cancellation over affine varieties
\inbook Modules and algebraic groups
\serial Zap. Nauchn. Sem. LOMI
\yr 1982
\vol 114
\pages 187--195
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl1778}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=669571}
\zmath{https://zbmath.org/?q=an:0569.14006|0499.14004}
\transl
\jour J. Soviet Math.
\yr 1984
\vol 27
\issue 4
\pages 2974--2980
\crossref{https://doi.org/10.1007/BF01410752}
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  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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