Riemann-Roch for homotopy invariant K-theory and Gysin morphisms

@article{Navarro2016RiemannRochFH,
  title={Riemann-Roch for homotopy invariant K-theory and Gysin morphisms},
  author={Alberto Navarro},
  journal={arXiv: K-Theory and Homology},
  year={2016}
}
  • A. Navarro
  • Published 3 May 2016
  • Mathematics
  • arXiv: K-Theory and Homology
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… 
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