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arXiv · 1911.01776

Enumerating Non-Stable Vector Bundles

Peng Du
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Abstract

In this article, we establish a motivic analog of an enumeration result of James-Thomas on non-stable vector bundles in topological setting. Using this, we obtain results on enumeration of projective modules of rank $d$ over a smooth affine $k$-algebra $A$ of dimension $d$, recovering in particular results of Suslin and Bhatwadekar on cancellation of such vector bundles. Admitting a conjecture of Asok and Fasel, we prove cancellation of such vector bundles of rank $d-1$ if the base field $k$ is algebraically closed. We also explore the cancellation properties of symplectic vector bundles.

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Peng Du. 2019-11-05. Enumerating Non-Stable Vector Bundles. https://doi.org/10.1093/imrn%2Frnab103

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