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Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 114, Pages 187–195
(Mi znsl1778)
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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.
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
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https://www.mathnet.ru/eng/znsl1778 https://www.mathnet.ru/eng/znsl/v114/p187
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