Algebraic vector bundles and -local A^1-homotopy theory
arXiv:2008.03363
Abstract
Using techniques of A^1-homotopy theory, we produce motivic lifts of elements in classical homotopy groups of spheres; these lifts provide polynomial maps of spheres and allow us to construct ``low rank'' algebraic vector bundles on ``simple'' smooth affine varieties of high dimension.
20 pages; Version to appear in Ann. Scient. Ec. Norm. Sup
References in corpus (7)
- From algebraic cobordism to motivic cohomology
- Motivic cell structures
- A cohomological classification of vector bundles on smooth affine threefolds
- Affine representability results in A^1-homotopy theory II: principal bundles and homogeneous spaces
- Etale realization on the A^1-homotopy theory of schemes
- Enumerating Non-Stable Vector Bundles
- Algebraic vs. topological vector bundles on spheres