Duality theorem for motives
Algebra i analiz, Tome 21 (2009) no. 2, pp. 205-213.

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

A general duality theorem for the category of motives is established, with a short, simple, and self-contained proof.
Keywords: category of motives, Poincaré duality, smooth algebraic varieties.
@article{AA_2009_21_2_a7,
     author = {I. A. Panin and S. A. Yagunov},
     title = {Duality theorem for motives},
     journal = {Algebra i analiz},
     pages = {205--213},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2009_21_2_a7/}
}
TY  - JOUR
AU  - I. A. Panin
AU  - S. A. Yagunov
TI  - Duality theorem for motives
JO  - Algebra i analiz
PY  - 2009
SP  - 205
EP  - 213
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2009_21_2_a7/
LA  - ru
ID  - AA_2009_21_2_a7
ER  - 
%0 Journal Article
%A I. A. Panin
%A S. A. Yagunov
%T Duality theorem for motives
%J Algebra i analiz
%D 2009
%P 205-213
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2009_21_2_a7/
%G ru
%F AA_2009_21_2_a7
I. A. Panin; S. A. Yagunov. Duality theorem for motives. Algebra i analiz, Tome 21 (2009) no. 2, pp. 205-213. http://geodesic.mathdoc.fr/item/AA_2009_21_2_a7/

[1] Adams J. F., Stable homotopy and generalized homology, Univ. of Chicago Press, Chicago–London, 1974 | MR

[2] Dold A., Puppe D., “Dvoistvennost, sled i transfer”, Tr. MIAN, 154, Nauka, M., 1983, 81–97 | MR

[3] Fomenko A., Fuks D., Kurs gomotopicheskoi topologii, Nauka, M., 1989 | MR

[4] Friedlander E., Voevodsky V., “Bivariant cycle cohomology”, Cycles, Transfers, and Motivic Homology Theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 138–187 | MR | Zbl

[5] Manin Yu. I., “Sootvetstviya, motivy i monoidalnye preobrazovaniya”, Mat. sb., 77(119):4 (1968), 475–507 | MR | Zbl

[6] May J. P., “The additivity of traces in triangulated categories”, Adv. Math., 163:1 (2001), 34–73 | DOI | MR | Zbl

[7] Mazza C., Voevodsky V., Weibel C., Lecture notes on motivic cohomology, Clay Math. Monogr., 2, Amer. Math. Soc., Providence, RI; Clay Math. Inst., Cambridge, MA, 2006 | MR | Zbl

[8] Panin I., Yagunov S., “$T$-spectra and Poincaré duality”, J. Reine Angew. Math., 617 (2008), 193–213 | MR | Zbl

[9] Poincaré H., “Analysis situs”, J. École Polytech., 1 (1895), 1–121 | MR

[10] Suslin A., Voevodsky V., “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., 548, Kluwer Acad. Publ., Dordrecht, 2000, 117–189 | MR | Zbl

[11] Voevodsky V., “Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic”, Int. Math. Res. Not., 2002:7 (2002), 351–355 | DOI | MR | Zbl

[12] Voevodsky V., “Triangulated categories of motives over a field”, Cycles, Transfers, and Motivic Homology Theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 188–238 | MR | Zbl