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St. Petersburg Mathematical Journal

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



Traces in oriented homology theories of algebraic varieties

Author: K. Pimenov
Translated by: the author
Original publication: Algebra i Analiz, tom 19 (2007), nomer 5.
Journal: St. Petersburg Math. J. 19 (2008), 805-828
MSC (2000): Primary 14F43
Published electronically: June 27, 2008
MathSciNet review: 2381946
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Abstract: This paper is an attempt to axiomatize the notion of oriented homology theory. Under the axioms in question, a Chern structure determines an orientation and vice versa. The main result of the paper is the projective bundle theorem in §2.

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

  • [Ne] Alexander Nenashev, Projective bundle theorem in homology theories with Chern structure, Doc. Math. 9 (2004), 487–497. MR 2117424
  • [P1] I. Panin, Oriented cohomology theories of algebraic varieties, 𝐾-Theory 30 (2003), no. 3, 265–314. Special issue in honor of Hyman Bass on his seventieth birthday. Part III. MR 2064242,
  • [PS] I. Panin and A. Smirnov, Push-forwards in oriented cohomology theories of algebraic varieties, (2000),
  • [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,
  • [Pi] K. Pimenov, Traces in oriented homology theories, (2005), 0724.
  • [PY] I. Panin and S. Yagunov, Poincaré duality for algebraic varieties, (2002), http://www.math.uiuc. edu/K-theory/0576.
  • [S] A. Solynin, Chern and Thom elements in the representable cohomology theories, Preprint POMI-03/2004;
  • [SV] Andrei Suslin and Vladimir Voevodsky, Bloch-Kato conjecture and motivic cohomology with finite coefficients, The arithmetic and geometry of algebraic cycles (Banff, AB, 1998) NATO Sci. Ser. C Math. Phys. Sci., vol. 548, Kluwer Acad. Publ., Dordrecht, 2000, pp. 117–189. MR 1744945
  • [V] V. Voevodsky, The Milnor conjecture, (1996),
  • [V1] Vladimir Voevodsky, 𝐀¹-homotopy theory, Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998), 1998, pp. 579–604. MR 1648048
  • [V2] -, Cancellation theorem, (2002)

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Additional Information

K. Pimenov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia

Keywords: Chern class, Thom isomorphism, orientation, homology theory
Received by editor(s): April 10, 2007
Published electronically: June 27, 2008
Additional Notes: Supported by the Russian Ministry of Education (grant no. PD02-1.1-368) and by INTAS (grant no. 05-1000008-8118)
Dedicated: Dedicated to the centenary of the birth of Dmitriĭ Konstantinovich Faddeev
Article copyright: © Copyright 2008 American Mathematical Society

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