Duality theorem for motives
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I. A. Panin and S. A. Yagunov
Translated by: The authors - St. Petersburg Math. J. 21 (2010), 309-315
- DOI: https://doi.org/10.1090/S1061-0022-10-01096-4
- Published electronically: January 26, 2010
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Abstract:
A general duality theorem for the category of motives is established, with a short, simple, and self-contained proof.References
- J. F. Adams, Stable homotopy and generalised homology, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0402720
- Albrecht Dold and Dieter Puppe, Duality, trace, and transfer, Proceedings of the International Conference on Geometric Topology (Warsaw, 1978) PWN, Warsaw, 1980, pp. 81–102. MR 656721
- A. T. Fomenko and D. B. Fuks, Kurs gomotopicheskoĭ topologii, “Nauka”, Moscow, 1989 (Russian). With an English summary. MR 1027592
- Eric M. Friedlander and Vladimir Voevodsky, Bivariant cycle cohomology, Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., vol. 143, Princeton Univ. Press, Princeton, NJ, 2000, pp. 138–187. MR 1764201
- Ju. I. Manin, Correspondences, motifs and monoidal transformations, Mat. Sb. (N.S.) 77 (119) (1968), 475–507 (Russian). MR 0258836
- J. P. May, The additivity of traces in triangulated categories, Adv. Math. 163 (2001), no. 1, 34–73. MR 1867203, DOI 10.1006/aima.2001.1995
- Carlo Mazza, Vladimir Voevodsky, and Charles Weibel, Lecture notes on motivic cohomology, Clay Mathematics Monographs, vol. 2, American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2006. MR 2242284
- Ivan Panin and Serge Yagunov, $T$-spectra and Poincaré duality, J. Reine Angew. Math. 617 (2008), 193–213. MR 2400995, DOI 10.1515/CRELLE.2008.030
- H. Poincaré, Analysis situs, J. École Polytech. 1 (1895), 1–121.
- 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
- Vladimir Voevodsky, Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic, Int. Math. Res. Not. 7 (2002), 351–355. MR 1883180, DOI 10.1155/S107379280210403X
- Vladimir Voevodsky, Triangulated categories of motives over a field, Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., vol. 143, Princeton Univ. Press, Princeton, NJ, 2000, pp. 188–238. MR 1764202
Bibliographic Information
- I. A. Panin
- Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
- Address at time of publication: Fakultät für Mathematik, Universität Bielefeld, Universitätstrasse, 25, Bielefeld 33615, Germany
- MR Author ID: 238161
- Email: panin@pdmi.ras.ru
- S. A. Yagunov
- Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
- Address at time of publication: Fakultät für Mathematik, Universität Bielefeld, Universitätstrasse, 25, Bielefeld 33615, Germany
- MR Author ID: 626515
- Email: yagunov@gmail.com
- Received by editor(s): September 25, 2008
- Published electronically: January 26, 2010
- Additional Notes: Both authors are deeply grateful to SFB-701 for its financial support during their work.
- © Copyright 2010 American Mathematical Society
- Journal: St. Petersburg Math. J. 21 (2010), 309-315
- MSC (2000): Primary 14F42
- DOI: https://doi.org/10.1090/S1061-0022-10-01096-4
- MathSciNet review: 2553047