Geodesic
Secondary characteristic classes and the Euler class
Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 7-29.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We then show that if $X$ is a smooth affine scheme of dimension $d$ over a field $k$ of finite 2-cohomological dimension (with $\mathrm{char}(k)\neq 2)$ and $E$ is a rank $d$ vector bundle over $X$, vanishing of the Chow-Witt theoretic Euler class of $E$ is equivalent to vanishing of its top Chern class and these higher classes. We then derive some consequences of our main theorem when $k$ is of small 2-cohomological dimension.
Classification : 14F42, 14C15, 13C10, 55S20 
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     author = {Asok, Aravind and Fasel, Jean},
     title = {Secondary characteristic classes and the {Euler} class},
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Asok, Aravind; Fasel, Jean. Secondary characteristic classes and the Euler class. Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 7-29. http://geodesic.mathdoc.fr/item/DOCMA_2015__S2__a22/