The Chow ring of a classifying space

Details The Chow ring of a classifying space The Chow ring of a classifying space

1998-02-20

arxiv.org/abs/math/9802097v1

Mathematics

Algebraic Geometry

34 pages, latex2e, to be published in Proc. Symp. Pure Math. (K-Theory, 1997) Apply "gunzip" and then "tar -xvf" to the file

Scientific paper

We define the Chow ring of the classifying space of a linear algebraic group. In all the examples where we can compute it, such as the symmetric groups and the orthogonal groups, it is isomorphic to a natural quotient of the complex cobordism ring of the classifying space, a topological invariant. We apply this to get torsion information on the Chow groups of varieties defined as quotients by finite groups. This generalizes Atiyah and Hirzebruch's use of such varieties to give counterexamples to the Hodge conjecture with integer coefficients.

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