Equivariant intersection theory
Abstract
In this paper we develop an equivariant intersection theory for actions of algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow groups. They are algebraic analogues of equivariant cohomology groups which satsify the formal properties of ordinary Chow groups. In addition, they enjoy many of the properties of equivariant cohomology. The principal results are: (1) We prove the existence of canonical intersection products on the Chow groups of geometric quotients of smooth varieties even when the stabilizers of geometric points are nonreduced. (2) We construct a Todd class map from equivariant $K$theory of coherent sheaves to a completion of equivariant Chow groups, and prove that a completion of equivariant $K$theory is isomorphic to the completion of equivariant Chow groups. (3) We prove a localization theorem for torus actions and use it to give a characteristic free proof of the Bott residue formula for actions of tori on complete smooth varieties.
 Publication:

arXiv eprints
 Pub Date:
 March 1996
 arXiv:
 arXiv:alggeom/9603008
 Bibcode:
 1996alg.geom..3008E
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 LaTex. 49pages. This paper subsumes our previous preprint "Equivariant Chow groups and the Bott residue formula", alggeom/9508001. Email for William Graham is wag@math.uchicago.edu. This revision corrects some minor errors and adds some references