%0 Journal Article
%@ 0002-9947
%A Navarro Garmendia, Alberto
%A Navarro Garmendia, JosÃ©
%D 2020
%F upm:67845
%J Transactions of the American Mathematical Society
%N 2
%P 755-772
%T On the Riemann-Roch formula without projective hypothesis
%U https://oa.upm.es/67845/
%V 374
%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.