Riemann-Roch for algebraic versus topological K-theory
The paper extends the work of Dwyer and Friedlander about etale K-theory by defining a mod \(\ell^{\nu}\) topological K-homology theory for quasiprojective schemes X over k (k is a ''nice'' noetherian ring in which the prime \(\ell\) is invertible). There is a natural transformation \(\rho\) (X) from algebraic G-theory to (mod \(\ell^{\nu})\) topological K- homology theory. The Riemann-Roch theorem says that \(\rho\) (X) is natural for projective morphisms. Most part of the paper is concerned with the definition of this topological K-homology theory. After that, the deformation to the normal cone machinery is adapted to prove the theorem. The results are applied to compute the algebraic and topological K-groups of reductive group schemes, homogeneous spaces and complete rational surfaces.
scientific article; zbMATH DE number 3867482
scientific article