1999/05/13 by Dan Edidin, Edidin, Dan, William Graham +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.math/9905081
openalex publication_date 1999/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to prove an equivariant Riemann-Roch theorem for schemes or algebraic spaces with an action of a linear algebraic group G. For a G-space X, this theorem gives an isomorphism between a completion of the equivariant Grothendieck group and a completion of equivariant equivariant Chow groups. The key to proving this isomorphism is a geometric description of completions of the equivariant Grothendieck group. Besides Riemann-Roch, this result has some purely K-theoretic applications. In particular, we prove a conjecture of Köck (in the case of regular schemes) and extend to arbitrary characteristic a result of Segal on representation rings.