A Riemann-roch Theorem for Flat Bundles, with Values in the Algebraic Chern-simons Theory Spencer Bloch and Hélène Esnault

Riemann-roch for Equivariant K-theory

The goal of this paper is to prove the equivariant version of Bloch’s Riemann-Roch isomorphism between the higher algebraic K-theory and the higher Chow groups of smooth varieties. We show that for a linear algebraic group G acting on a smooth variety X , although there is no Chern character map from the equivariant K-groups to equivariant higher Chow groups, there is indeed such a map K i (X)⊗...

Lectures on Algebro-geometric Chern-weil and Cheeger-chern-simons Theory for Vector Bundles

A Parametrized Index Theorem for the Algebraic

Riemann-Roch theorems assert that certain algebraically defined wrong way maps (transfers) in algebraic K–theory agree with topologically defined ones [BaDo]. Bismut and Lott [BiLo] proved such a Riemann–Roch theorem where the wrong way maps are induced by the projection of a smooth fiber bundle, and the topologically defined transfer map is the Becker–Gottlieb transfer. We generalize and refin...

A PARAMETERIZED INDEX THEOREM FOR THE ALGEBRAIC K-THEORY EULER CLASS W.Dwyer, M.Weiss, B.Williams

A Riemann-Roch theorem asserts that some algebraically defined wrong– way map in K-theory agrees with a topologically defined one [BFM]. Bismut and Lott [BiLo] proved a Riemann–Roch theorem for smooth fiber bundles in which the topologically defined wrong–way map is the homotopy transfer of Becker–Gottlieb and Dold. We generalize their theorem, refine it, and prove a converse stating that an ap...

Riemann–roch Theorem for Operations in Cohomology of Algebraic Varieties

The Riemann–Roch theorem for multiplicative operations in oriented cohomology theories for algebraic varieties is proved and an explicit formula for the corresponding Todd classes is given. The formula obtained can also be applied in the topological situation, and the theorem can be regarded as a change-of-variables formula for the integration of cohomology classes. The classical Riemann–Roch t...