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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.