On Stably Free Modules over Affine Algebras
Publications Mathématiques de l'IHÉS, Volume 116 (2012), pp. 223-243.

If X is a smooth affine variety of dimension d over an algebraically closed field k, and if (d−1)!∈k × then any stably trivial vector bundle of rank (d−1) over X is trivial. The hypothesis that X is smooth can be weakened to X is normal if d≥4.

DOI: 10.1007/s10240-012-0041-y
Fasel, J. 1; Rao, R. A. 2; Swan, R. G. 3

1 Mathematisches Institut der Universität München Theresienstrasse 39, 80333, München Germany
2 Tata Institute of Fundamental Research 1, Dr. Homi Bhabha Road, Navy Nagar, Mumbai, 400 005 India
3 University of Chicago Chicago, IL, 60637 USA
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Fasel, J.; Rao, R. A.; Swan, R. G. On Stably Free Modules over Affine Algebras. Publications Mathématiques de l'IHÉS, Volume 116 (2012), pp. 223-243. doi : 10.1007/s10240-012-0041-y. http://www.numdam.org/articles/10.1007/s10240-012-0041-y/

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