Algebraic vector bundles and $p$-local A^1-homotopy theory
Algebraic Geometry
2025-04-11 v3 Algebraic Topology
K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.2008.03363,
title = {Algebraic vector bundles and $p$-local A^1-homotopy theory},
author = {Aravind Asok and Jean Fasel and Michael J. Hopkins},
journal= {arXiv preprint arXiv:2008.03363},
year = {2025}
}
Comments
20 pages; Version to appear in Ann. Scient. Ec. Norm. Sup