On stably free modules over affine algebras

Fasel, J. ; Rao, R. A. ; Swan, R. G. (2012) On stably free modules over affine algebras Publications Mathematiques de L'IHES, 116 (1). pp. 223-243. ISSN 0073-8301

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Official URL: http://link.springer.com/article/10.1007/s10240-01...

Related URL: http://dx.doi.org/10.1007/s10240-012-0041-y

Abstract

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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