Characteristic classes in the Chow ring

Details Characteristic classes in the Chow ring Characteristic classes in the Chow ring

1994-12-10

arxiv.org/abs/alg-geom/9412008v1

Mathematics

Algebraic Geometry

12pages, LaTeX

Scientific paper

We study the ring of characteristic classes with values in the Chow ring for principal $G$-bundles over schemes. If we consider bundles which are locally trivial in the Zariski topology, then we show, for $G$ reductive, that this ring is isomorphic to the Weyl group invariants in the algebra generated by characters of the maximal torus. For general principal bundles the same isomorphism holds after tensoring the coefficients with ${\Bbb Q}$. As a corollary, we show that any (non-torsion) topological characteristic class is algebraic when applied to Zariski locally trivial bundles over complex algebraic varieties.

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