Cancellation over affine varieties

A. A. Suslin

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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 languageEnglish (US)
Pages (from-to)2974-2980
Number of pages7
JournalJournal of Soviet Mathematics
Issue number4
StatePublished - Nov 1984

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Applied Mathematics


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