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1 November 2014 A cohomological classification of vector bundles on smooth affine threefolds
Aravind Asok, Jean Fasel
Duke Math. J. 163(14): 2561-2601 (1 November 2014). DOI: 10.1215/00127094-2819299

Abstract

We give a cohomological classification of vector bundles of rank 2 on a smooth affine threefold over an algebraically closed field having characteristic unequal to 2. As a consequence we deduce that cancellation holds for rank 2 vector bundles on such varieties. The proofs of these results involve three main ingredients. First, we give a description of the first nonstable A1-homotopy sheaf of the symplectic group. Second, these computations can be used in concert with F. Morel’s A1-homotopy classification of vector bundles on smooth affine schemes and obstruction theoretic techniques (stemming from a version of the Postnikov tower in A1-homotopy theory) to reduce the classification results to cohomology vanishing statements. Third, we prove the required vanishing statements.

Citation

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Aravind Asok. Jean Fasel. "A cohomological classification of vector bundles on smooth affine threefolds." Duke Math. J. 163 (14) 2561 - 2601, 1 November 2014. https://doi.org/10.1215/00127094-2819299

Information

Published: 1 November 2014
First available in Project Euclid: 31 October 2014

zbMATH: 1314.14044
MathSciNet: MR3273577
Digital Object Identifier: 10.1215/00127094-2819299

Subjects:
Primary: 14F42
Secondary: 13C10, 19A13, 19D45, 55S35

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 14 • 1 November 2014
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