RT Journal Article
SR 00
ID 10.1090/tran/8107
A1 Navarro Garmendia, Alberto
A1 Navarro Garmendia, JosÃ©
T1 On the Riemann-Roch formula without projective hypothesis
JF Transactions of the American Mathematical Society
YR 2020
FD 2020-11-03
VO 374
IS 2
SP 755
OP 772
AB 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
LK https://oa.upm.es/67845/
UL https://www.ams.org/journals/tran/2021-374-02/S0002-9947-2020-08107-0/