English

Comparing Euler classes

Algebraic Geometry 2016-08-17 v2 Commutative Algebra Algebraic Topology K-Theory and Homology

Abstract

We establish the equality of two definitions of an Euler class in algebraic geometry: the first definition is as a "characteristic class" with values in Chow-Witt theory, while the second definition is as an "obstruction class." Along the way, we refine Morel's relative Hurewicz theorem in A^1-homotopy theory, and show how to define (twisted) Chow-Witt groups for geometric classifying spaces.

Keywords

Cite

@article{arxiv.1306.5250,
  title  = {Comparing Euler classes},
  author = {Aravind Asok and Jean Fasel},
  journal= {arXiv preprint arXiv:1306.5250},
  year   = {2016}
}

Comments

33 pages; Final version (before proofs). To appear Q. J. Math

R2 v1 2026-06-22T00:38:22.915Z