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.
@article{PMIHES_2012__116__223_0, author = {Fasel, J. and Rao, R. A. and Swan, R. G.}, title = {On {Stably} {Free} {Modules} over {Affine} {Algebras}}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {223--243}, publisher = {Springer-Verlag}, volume = {116}, year = {2012}, doi = {10.1007/s10240-012-0041-y}, mrnumber = {3090257}, zbl = {1256.13008}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-012-0041-y/} }
TY - JOUR AU - Fasel, J. AU - Rao, R. A. AU - Swan, R. G. TI - On Stably Free Modules over Affine Algebras JO - Publications Mathématiques de l'IHÉS PY - 2012 SP - 223 EP - 243 VL - 116 PB - Springer-Verlag UR - http://www.numdam.org/articles/10.1007/s10240-012-0041-y/ DO - 10.1007/s10240-012-0041-y LA - en ID - PMIHES_2012__116__223_0 ER -
%0 Journal Article %A Fasel, J. %A Rao, R. A. %A Swan, R. G. %T On Stably Free Modules over Affine Algebras %J Publications Mathématiques de l'IHÉS %D 2012 %P 223-243 %V 116 %I Springer-Verlag %U http://www.numdam.org/articles/10.1007/s10240-012-0041-y/ %R 10.1007/s10240-012-0041-y %G en %F PMIHES_2012__116__223_0
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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