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The purpose of this paper is to develop an equivariant intersection theory for actions of linear 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 have all the functorial properties of ordinary Chow groups. In addition, they enjoy(More)
Let G be a reductive algebraic group over an algebraically closed field k. An algebraic characteristic class of degree i for principal G-bundles on schemes is a function c assigning to each principal G-bundle E → X an element c(E) in the Chow group A i X, natural with respect to pullbacks. These classes are analogous to topological characteristic classes(More)
We prove a localization formula in equivariant algebraic K-theory for an arbitrary complex algebraic group acting with finite stabilizer on a smooth algebraic space. This extends to non-diagonalizable groups the localization formulas of H.A. Nielsen [Nie] and R. Thomason [Tho5] As an application we give a Riemann-Roch formula for quotients of smooth(More)
Let V be a rank N vector bundle on a d-dimensional complex projective scheme X; assume that V is equipped with a skew-symmetric bilinear form with values in a line bundle L and that Λ 2 V * ⊗L is ample. Suppose that the maximum rank of the form at any point of X is r, where r > 0 is even. The main result of this paper is that if d > 2(N − r), then the locus(More)
We prove a positivity property for the cup product in the T-equivariant cohomology of the flag variety. This was conjectured by D. Peterson and has as a consequence a conjecture of S. Billey. The result for the flag variety follows from a more general result about algebraic varieties with an action of a solvable linear algebraic group such that the(More)
2000, is a preliminary version of a paper to be presented at a University of Pennsylvania Law School conference on Norms and Corporate Law in December, 2000. A later version will include more complete footnotes. I am grateful for excellent suggestions received from Henry Smith and George Triantis. Interested readers can contact s-levmore@uchicago.edu, where(More)