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 étale cohomology group Het3(X,ΜeF{cyrillic}2) 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.
Original language | English (US) |
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Pages (from-to) | 2974-2980 |
Number of pages | 7 |
Journal | Journal of Soviet Mathematics |
Volume | 27 |
Issue number | 4 |
DOIs | |
State | Published - Nov 1984 |
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Applied Mathematics