On Stably Free Modules over Affine Algebras
Publications Mathématiques de l'IHÉS, Tome 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.

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     title = {On {Stably} {Free} {Modules} over {Affine} {Algebras}},
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Fasel, J.; Rao, R. A.; Swan, R. G. On Stably Free Modules over Affine Algebras. Publications Mathématiques de l'IHÉS, Tome 116 (2012), pp. 223-243. doi : 10.1007/s10240-012-0041-y. http://archive.numdam.org/articles/10.1007/s10240-012-0041-y/

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