English

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