arXiv Analytics

Sign in

arXiv:math/9802097 [math.AG]AbstractReferencesReviewsResources

The Chow ring of a classifying space

Burt Totaro

Published 1998-02-20Version 1

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.

Comments: 34 pages, latex2e, to be published in Proc. Symp. Pure Math. (K-Theory, 1997) Apply "gunzip" and then "tar -xvf" to the file
Categories: math.AG
Subjects: 14C25, 14L30, 20J06, 55N22
Related articles: Most relevant | Search more
arXiv:math/0411424 [math.AG] (Published 2004-11-19)
The Chow ring of the classifying space $BSO(2n,{\mathbb C})$
arXiv:math/0505052 [math.AG] (Published 2005-05-03, updated 2005-07-03)
On the cohomology and the Chow ring of the classifying space of PGL_p
arXiv:1405.4084 [math.AG] (Published 2014-05-16)
The Chow ring for the classifying space of $GO(2n)$

Links

Toolbox