Geodesic
On Stably Free Modules over Affine Algebras
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

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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.

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 
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     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},
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     year = {2012},
     doi = {10.1007/s10240-012-0041-y},
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     zbl = {1256.13008},
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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

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