%N 2
%X Let S be a finite dimensional noetherian scheme. For any proper morphism between smooth S-schemes, we prove a Riemann-Roch formula relating higher algebraic K-theory and motivic cohomology, thus with no projective hypothesis neither on the schemes nor on the morphism. We also prove, without projective assumptions, an arithmetic Riemann-Roch theorem involving Arakelov?s higher K-theory and motivic cohomology as well as an analogue result for the relative cohomology of a morphism. These results are obtained as corollaries of a motivic statement that is valid for morphisms between oriented absolute spectra in the stable homotopy category of S.
%R 10.1090/tran/8107
%A Alberto Navarro Garmendia
%A JosÃ© Navarro Garmendia
%D 2020
%T On the Riemann-Roch formula without projective hypothesis
%P 755-772
%I Arquitectura
%L upm67845
%V 374
%J Transactions of the American Mathematical Society