2021-09-03T05:47:42Z
2021-09-03T05:47:42Z
https://oa.upm.es/id/eprint/67845
This item is in the repository with the URL: https://oa.upm.es/id/eprint/67845
2021-09-03T05:47:42Z
On the Riemann-Roch formula without projective hypothesis
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.
Alberto Navarro Garmendia
JosÃ© Navarro Garmendia