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.
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DOI: 10.1007/s10240-012-0041-y
J. Fasel 1; R. A. Rao 2; R. G. Swan 3
@article{PMIHES_2012__116__223_0,
author = {J. Fasel and R. A. Rao and R. G. Swan},
title = {On {Stably} {Free} {Modules} over {Affine} {Algebras}},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {223--243},
year = {2012},
publisher = {Springer-Verlag},
volume = {116},
doi = {10.1007/s10240-012-0041-y},
mrnumber = {3090257},
zbl = {1256.13008},
language = {en},
url = {https://pmihes.centre-mersenne.org/articles/10.1007/s10240-012-0041-y/}
}
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%0 Journal Article %A J. Fasel %A R. A. Rao %A R. G. Swan %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 https://pmihes.centre-mersenne.org/articles/10.1007/s10240-012-0041-y/ %R 10.1007/s10240-012-0041-y %G en %F PMIHES_2012__116__223_0
J. Fasel; R. A. Rao; R. G. Swan. 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
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