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), 805828
MSC (2000):
Primary 14F43
Published electronically:
June 27, 2008
MathSciNet review:
2381946
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
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.
 [Ne]
Alexander
Nenashev, Projective bundle theorem in homology theories with Chern
structure, Doc. Math. 9 (2004), 487–497
(electronic). MR
2117424 (2006f:14021)
 [P1]
I.
Panin, Oriented cohomology theories of algebraic varieties,
𝐾Theory 30 (2003), no. 3, 265–314.
Special issue in honor of Hyman Bass on his seventieth birthday. Part III.
MR
2064242 (2005f:14043), http://dx.doi.org/10.1023/B:KTHE.0000019788.33790.cb
 [PS]
I. Panin and A. Smirnov, Pushforwards in oriented cohomology theories of algebraic varieties, (2000), http://www.math.uiuc.edu/Ktheory/0459.
 [Pa]
I.
Panin, RiemannRoch 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
(2005g:14025), http://dx.doi.org/10.1007/9789400709485_8
 [Pi]
K. Pimenov, Traces in oriented homology theories, (2005), http://www.math.uiuc.edu/Ktheory/ 0724.
 [PY]
I. Panin and S. Yagunov, Poincaré duality for algebraic varieties, (2002), http://www.math.uiuc. edu/Ktheory/0576.
 [S]
A. Solynin, Chern and Thom elements in the representable cohomology theories, Preprint POMI03/2004; www.pdmi.ras.ru/preprint.
 [SV]
Andrei
Suslin and Vladimir
Voevodsky, BlochKato 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
(2001g:14031)
 [V]
V. Voevodsky, The Milnor conjecture, (1996), http://www.math.uiuc.edu/Ktheory/0170.
 [V1]
Vladimir
Voevodsky, 𝐀¹homotopy theory, Proceedings of the
International Congress of Mathematicians, Vol. I (Berlin, 1998), 1998,
pp. 579–604 (electronic). MR 1648048
(99j:14018)
 [V2]
, Cancellation theorem, (2002) http://www.math.uiuc.edu/Ktheory/0541.
 [Ne]
 A. Nenashev, Projective bundle theorem in homology theories with Chern structure, Doc. Math. 9 (2004), 487497 (electronic). MR 2117424 (2006f:14021)
 [P1]
 I. Panin, Oriented cohomology theories of algebraic varieties, KTheory 30 (2003), no. 3, 265314. MR 2064242 (2005f:14043)
 [PS]
 I. Panin and A. Smirnov, Pushforwards in oriented cohomology theories of algebraic varieties, (2000), http://www.math.uiuc.edu/Ktheory/0459.
 [Pa]
 I. Panin, RiemannRoch theorems for oriented cohomology, Axiomatic, Enriched, and Motivic Homotopy Theory, NATO Sci. Ser. II Math. Phys. Chem., vol. 131, Kluwer Acad. Publ., Dordrecht, 2004. MR 2061857 (2005g:14025)
 [Pi]
 K. Pimenov, Traces in oriented homology theories, (2005), http://www.math.uiuc.edu/Ktheory/ 0724.
 [PY]
 I. Panin and S. Yagunov, Poincaré duality for algebraic varieties, (2002), http://www.math.uiuc. edu/Ktheory/0576.
 [S]
 A. Solynin, Chern and Thom elements in the representable cohomology theories, Preprint POMI03/2004; www.pdmi.ras.ru/preprint.
 [SV]
 A. Suslin and V. Voevodsky, BlochKato 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. 117189. MR 1744945 (2001g:14031)
 [V]
 V. Voevodsky, The Milnor conjecture, (1996), http://www.math.uiuc.edu/Ktheory/0170.
 [V1]
 , homotopy theory, Doc. Math. 1998, Extra Vol. I, 579604 (electronic). MR 1648048 (99j:14018)
 [V2]
 , Cancellation theorem, (2002) http://www.math.uiuc.edu/Ktheory/0541.
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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
Email:
kip302002@yahoo.com
DOI:
http://dx.doi.org/10.1090/S1061002208010224
PII:
S 10610022(08)010224
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. PD021.1368) and by INTAS (grant no. 0510000088118)
Dedicated:
Dedicated to the centenary of the birth of Dmitriĭ Konstantinovich Faddeev
Article copyright:
© Copyright 2008
American Mathematical Society
