Secondary characteristic classes and the Euler class

  • Aravind Asok

  • Jean Fasel


We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We then show that if is a smooth affine scheme of dimension over a field of finite 2-cohomological dimension (with and is a rank vector bundle over , vanishing of the Chow-Witt theoretic Euler class of is equivalent to vanishing of its top Chern class and these higher classes. We then derive some consequences of our main theorem when is of small 2-cohomological dimension.