2016/05/03 by Navarro, Alberto
#14C40 #19D99 #19E20 #19L10 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.1605.00980
We prove the Riemann-Roch theorem for homotopy invariant K-theory and projective local complete intersection morphisms between finite dimensional noetherian schemes, without smoothness assumptions. We also prove a new Riemann-Roch theorem for the relative cohomology of a morphism. In order to do so, we construct and characterize Gysin morphisms for regular immersions between cohomologies represented by spectra (examples include homotopy invariant K-theory, motivic cohomology, their arithmetic counterparts, real absolute Hodge and Deligne-Beilinson cohomology, rigid syntomic cohomology, mixed Weil cohomologies) and use this construction to prove a motivic version of the Riemann-Roch.