TY - JOUR
JF - Transactions of the American Mathematical Society
ID - upm67845
TI - On the Riemann-Roch formula without projective hypothesis
SP - 755
A1 - Navarro Garmendia, Alberto
A1 - Navarro Garmendia, José
UR - https://www.ams.org/journals/tran/2021-374-02/S0002-9947-2020-08107-0/
AV - public
Y1 - 2020/11/03/
VL - 374
EP - 772
IS - 2
N2 - 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.
SN - 0002-9947
ER -