Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



On the Riemann-Roch theorem without denominators

Authors: O. B. Podkopaev and E. K. Shinder
Translated by: O. B. Podkopaev
Original publication: Algebra i Analiz, tom 18 (2006), nomer 6.
Journal: St. Petersburg Math. J. 18 (2007), 1021-1027
MSC (2000): Primary 14C40
Published electronically: October 2, 2007
MathSciNet review: 2307360
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [Fu] W. Fulton, Intersection theory, Ergeb. Math. Grenzgeb. (3), Bd. 2, Springer-Verlag, Berlin, 1984. MR 0732620 (85k:14004)
  • [Gr] Alexander Grothendieck, La théorie des classes de Chern, Bull. Soc. Math. France 86 (1958), 137–154 (French). MR 0116023
  • [Har] Robin Hartshorne, Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR 0463157
  • [MS] John W. Milnor and James D. Stasheff, Characteristic classes, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. Annals of Mathematics Studies, No. 76. MR 0440554
  • [P1] I. Panin, Push-forwards in oriented cohomology theories of algebraic varieties: II,
  • [PS] I. Panin and A. Smirnov, Push-forwards in oriented cohomology theories of algebraic varieties,
  • [Pa] 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,
  • [Qu] Daniel Quillen, Higher algebraic 𝐾-theory. I, Algebraic 𝐾-theory, I: Higher 𝐾-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Springer, Berlin, 1973, pp. 85–147. Lecture Notes in Math., Vol. 341. MR 0338129
  • [Ve] J.-L. Verdier, Spécialisation des classes de Chern, Astérisque, No. 82-83, Soc. Math. France, Paris, 1981, pp. 149-159. MR 0629126 (83m:14015)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 14C40

Retrieve articles in all journals with MSC (2000): 14C40

Additional Information

O. B. Podkopaev

E. K. Shinder

Keywords: Riemann--Roch formula without denominators, deformation to the normal cone, Koszul complex, Chern classes, oriented cohomology pretheory
Received by editor(s): June 14, 2006
Published electronically: October 2, 2007
Additional Notes: Partially supported by CNRS, France
Article copyright: © Copyright 2007 American Mathematical Society

American Mathematical Society