Geodesic
Traces in oriented homology theories of algebraic varieties
Algebra i analiz, Tome 19 (2007) no. 5, pp. 179-213.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Chern class, Thom isomorphism, orientation, homology theory. 
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K. I. Pimenov. Traces in oriented homology theories of algebraic varieties. Algebra i analiz, Tome 19 (2007) no. 5, pp. 179-213. http://geodesic.mathdoc.fr/item/AA_2007_19_5_a7/

[1] Nenashev A., “Projective bundle theorem in homology theories with Chern structure”, Doc. Math., 9 (2004), 487–497 | MR | Zbl

[2] Panin I., “Oriented cohomology theories of algebraic varieties”, $K$-Theory, 30:3 (2003), 265–314 | MR | Zbl

[3] Panin I., Smirnov A., Push-forwards in oriented cohomology theories of algebraic varieties, http://www.math.uiuc.edu/K-theory/0459/2000

[4] Panin I., Axiomatic, Enriched, and Motivic Homotopy Theory, NATO Sci. Ser. II Math. Phys. Chem., 131, Kluwer Acad. Publ., Dordrecht, 2004 | MR | Zbl

[5] Pimenov K., Traces in oriented homology theories, http://www.math.uiuc.edu/K-theory/0724/2005

[6] Panin I., Yagunov S., Poincare duality for algebraic varieties, http://www.math.uiuc.edu/K-theory/0576/2002

[7] Solynin A., Chern and Thom elements in the representable cohomology theories, Preprint POMI-03/2004

[8] Suslin A., Voevodsky V., “Bloch–Kato conjecture and motivic cohomology with finite coefficients”, The Arithmetics and Geometry of Algebraic Cycles (Banff, AB, 1998), NATO Sci. Ser. C. Math. Phys. Sci., 548, Kluwer Acad. Publ., Dordrecht, 2000, 117–189 | MR | Zbl

[9] Voevodsky V., The Milnor conjecture, http://www.math.uiuc.edu/K-theory/0170/1996

[10] Voevodsky V., “$A^1$-homotopy theory”, Doc. Math., Extra Vol. I (1998), 579–604, electronic | MR | Zbl

[11] Voevodsky V., Cancellation theorem, http://www.math.uiuc.edu/K-theory/0541/2002