On the Riemann–Roch theorem without denominators

Podkopaev, O.; Shinder, E.

doi:10.1090/S1061-0022-07-00981-8

On the Riemann–Roch theorem without denominators
HTML articles powered by AMS MathViewer

by O. B. Podkopaev and E. K. Shinder
Translated by: O. B. Podkopaev

St. Petersburg Math. J. 18 (2007), 1021-1027

DOI: https://doi.org/10.1090/S1061-0022-07-00981-8

Published electronically: October 2, 2007

PDF | Request permission

Abstract:

A proof of the Riemann–Roch theorem without denominators is given. It is also proved that Grothendieck’s ring functor ${CH_{\operatorname {mult}}}$ is not an oriented cohomology pretheory.

References

William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620, DOI 10.1007/978-3-662-02421-8
Alexander Grothendieck, La théorie des classes de Chern, Bull. Soc. Math. France 86 (1958), 137–154 (French). MR 116023
Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554
I. Panin, Push-forwards in oriented cohomology theories of algebraic varieties: II, http://www.math.uiuc.edu/K-theory/0619/2003.
I. Panin and A. Smirnov, Push-forwards in oriented cohomology theories of algebraic varieties, http://www.math.uiuc.edu/K-theory/0459/2000.
I. Panin, Riemann-Roch theorems for oriented cohomology, Axiomatic, enriched and motivic homotopy theory, NATO Sci. Ser. II Math. Phys. Chem., vol. 131, Kluwer Acad. Publ., Dordrecht, 2004, pp. 261–333. MR 2061857, DOI 10.1007/978-94-007-0948-5_{8}
Daniel Quillen, Higher algebraic $K$-theory. I, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Lecture Notes in Math., Vol. 341, Springer, Berlin, 1973, pp. 85–147. MR 0338129
J.-L Verdier, Spécialisation des classes de Chern, The Euler-Poincaré characteristic (French), Astérisque, vol. 82, Soc. Math. France, Paris, 1981, pp. 149–159 (French). MR 629126