Comparing Euler classes

Aravind Asok (1) , Jean Fasel (2)

1 USC - University of Southern California
2 IF - Institut Fourier

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.

Domains: Algebraic Geometry [math.AG]; Commutative Algebra [math.AC]; Algebraic Topology [math.AT]; K-Theory and Homology [math.KT]; Mathematics [math]

Aravind Asok, Jean Fasel. Comparing Euler classes. Quarterly Journal of Mathematics, 2016, 67 (4), pp.603-635. ⟨10.1093/qmath/haw033⟩. ⟨hal-01674706⟩