Enumerating Non-Stable Vector Bundles
Peng Du

TL;DR
This paper develops a motivic analog of a topological enumeration result for non-stable vector bundles, leading to new insights on projective modules, cancellation properties, and symplectic bundles over algebraic varieties.
Contribution
It introduces a motivic framework for enumerating non-stable vector bundles and proves cancellation results under certain conditions, extending previous algebraic and topological findings.
Findings
Established a motivic analog of James-Thomas enumeration result
Proved cancellation of rank d-1 vector bundles over algebraically closed fields
Explored cancellation properties of symplectic vector bundles
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 over a smooth affine -algebra of dimension , 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 if the base field is algebraically closed. We also explore the cancellation properties of symplectic vector bundles.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry
