A residual Riemann-Roch formula

Abstract:  The Riemann-Roch theorem, and especially the formulation of Grothendieck, has long been interpreted in algebraic topology within the framework of oriented cohomology theories. I will explain how to use the homotopy theory of Morel and Voevodsky to get this kind of interpretation of the Riemann-Roch theorem formulated for arithmetic schemes. This work yields as a surprise a second Riemann-Roch formula which concerns residues rather than Gysin morphisms.