@article{upm67845,
         journal = {Transactions of the American Mathematical Society},
          volume = {374},
           title = {On the Riemann-Roch formula without projective hypothesis},
           month = {November},
          author = {Alberto Navarro Garmendia and Jos{\'e} Navarro Garmendia},
            year = {2020},
           pages = {755--772},
          number = {2},
             url = {https://oa.upm.es/67845/},
        abstract = {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.}
}