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arXiv · 1307.6831

Secondary characteristic classes and the Euler class

Aravind Asok·Jean Fasel
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Abstract

We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We show that if X is a smooth affine scheme of dimension d over a field k of finite 2-cohomological dimension (with 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.

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Aravind Asok, Jean Fasel. 2015-04-10. Secondary characteristic classes and the Euler class. https://arxiv.org/abs/1307.6831

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