On Stably Free Modules over Affine Algebras

Fasel, J.; Rao, R. A.; Swan, R. G.

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

Publications Mathématiques de l'IHÉS, Tome 116 (2012), pp. 223-243.

Résumé

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.

MR Zbl

DOI : 10.1007/s10240-012-0041-y

Affiliations des auteurs :

Fasel, J. ¹ ; Rao, R. A. ² ; Swan, R. G. ³

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     title = {On {Stably} {Free} {Modules} over {Affine} {Algebras}},
     journal = {Publications Math\'ematiques de l'IH\'ES},
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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://www.numdam.org/articles/10.1007/s10240-012-0041-y/

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