Abstract
It is proved that if X is a smooth affine curve over a field F of characteristic ≠l, then the group SK1(X)/l SK1(X) is isomorphic to a subgroup of the etale cohomology group H et 3 (X,Μ e Ф2 ) and if F is algebraically closed, then SK1(X) is a uniquely divisible group. The following cancellation theorem is obtained from results about SK1 for curves: If X is a normal affine variety of dimension n over a field F, and if char F > n and C.d.e(F)⩽1 for any prime l>/n then any stably trivial vector bundle of rank n over X is trivial.
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