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Book Review

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Book Information:

Authors: Vladimir Voevodsky, Andrei Suslin and Eric M. Friedlander
Title: Cycles, transfers, and motivic homology theories
Additional book information: Annals of Mathematics Studies, No. 143, Princeton Univ. Press, Princeton, NJ, 2000, 254 pp., ISBN 0-691-04815-0, $24.95, paperback

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

  • [Be1] A. A. Beĭlinson, Higher regulators and values of 𝐿-functions, Current problems in mathematics, Vol. 24, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1984, pp. 181–238 (Russian). MR 760999
  • [Be2] A. A. Beĭlinson, Notes on absolute Hodge cohomology, Applications of algebraic 𝐾-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 35–68. MR 862628, https://doi.org/10.1090/conm/055.1/862628
  • [Be3] A. Beilinson, Letter to Soulé, 1/11/1982.
  • [Be4] A. A. Beĭlinson, Height pairing between algebraic cycles, 𝐾-theory, arithmetic and geometry (Moscow, 1984–1986) Lecture Notes in Math., vol. 1289, Springer, Berlin, 1987, pp. 1–25. MR 923131, https://doi.org/10.1007/BFb0078364
  • [Bl] Spencer Bloch, Algebraic cycles and higher 𝐾-theory, Adv. in Math. 61 (1986), no. 3, 267–304. MR 852815, https://doi.org/10.1016/0001-8708(86)90081-2
  • [D] Pierre Deligne, Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 5–57 (French). MR 498551
  • [Dz] M. Demazure, Motifs de varietés algébriques, Sem. Bourbaki, vol. 365, 1969.
  • [FL] Eric M. Friedlander and H. Blaine Lawson, Moving algebraic cycles of bounded degree, Invent. Math. 132 (1998), no. 1, 91–119. MR 1618633, https://doi.org/10.1007/s002220050219
  • [Fr] Peter Freyd, Abelian categories. An introduction to the theory of functors, Harper’s Series in Modern Mathematics, Harper & Row, Publishers, New York, 1964. MR 0166240
  • [G57] Théorie des intersections et théorème de Riemann-Roch, Lecture Notes in Mathematics, Vol. 225, Springer-Verlag, Berlin-New York, 1971 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1966–1967 (SGA 6); Dirigé par P. Berthelot, A. Grothendieck et L. Illusie. Avec la collaboration de D. Ferrand, J. P. Jouanolou, O. Jussila, S. Kleiman, M. Raynaud et J. P. Serre. MR 0354655
  • [G64] A. Grothendieck, Letter to Serre, dated August 16, 1964, extracted in Annexe 1 of [S].
  • [G69] A. Grothendieck, Standard conjectures on algebraic cycles, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968), Oxford Univ. Press, London, 1969, pp. 193–199. MR 0268189
  • [G73] A. Grothendieck, Letter to Ilusie, dated May 3, 1973, Appendix to [J1].
  • [H] Masaki Hanamura, Mixed motives and algebraic cycles. I, Math. Res. Lett. 2 (1995), no. 6, 811–821. MR 1362972, https://doi.org/10.4310/MRL.1995.v2.n6.a12
  • [J1] Uwe Jannsen, Motivic sheaves and filtrations on Chow groups, Motives (Seattle, WA, 1991) Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 245–302. MR 1265533
  • [J2] Uwe Jannsen, Motives, numerical equivalence, and semi-simplicity, Invent. Math. 107 (1992), no. 3, 447–452. MR 1150598, https://doi.org/10.1007/BF01231898
  • [Le] Marc Levine, Mixed motives, Mathematical Surveys and Monographs, vol. 57, American Mathematical Society, Providence, RI, 1998. MR 1623774
  • [Li] S. Lichtenbaum, Values of zeta-functions at non-negative integers, Lecture Notes in Math., vol. 1068, Springer-Verlag, 1984, pp. 127-138. CMP 16:17
  • [K] Steven L. Kleiman, Motives, Algebraic geometry, Oslo 1970 (Proc. Fifth Nordic Summer-School in Math., Oslo, 1970) Wolters-Noordhoff, Groningen, 1972, pp. 53–82. MR 0382267
  • [M] Uwe Jannsen, Steven Kleiman, and Jean-Pierre Serre (eds.), Motives, Proceedings of Symposia in Pure Mathematics, vol. 55, American Mathematical Society, Providence, RI, 1994. MR 1265549
  • [Ma] Ju. I. Manin, Correspondences, motifs and monoidal transformations, Mat. Sb. (N.S.) 77 (119) (1968), 475–507 (Russian). MR 0258836
  • [Q] Daniel Quillen, Higher algebraic 𝐾-theory. I, Algebraic 𝐾-theory, I: Higher 𝐾-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Springer, Berlin, 1973, pp. 85–147. Lecture Notes in Math., Vol. 341. MR 0338129
  • [S] Jean-Pierre Serre, Motifs, Astérisque 198-200 (1991), 11, 333–349 (1992) (French, with English summary). Journées Arithmétiques, 1989 (Luminy, 1989). MR 1144336
  • [Sh] Richard Shiff, Sensation, movement, Cezanne, Classic Cezanne (Terence Maloon, ed.), Sydney, 1998, pp. 13-27.
  • [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, preprint (1996), www.math.uiuc.edu/K-theory/ 0170.

Review Information:

Reviewer: Charles A. Weibel
Affiliation: Rutgers University
Email: weibel@math.rutgers.edu
Journal: Bull. Amer. Math. Soc. 39 (2002), 137-143
MSC (2000): Primary 14F42; Secondary 19E15
Published electronically: October 12, 2001
Additional Notes: Weibel was partially supported by NSF grant DMS98-01560
Review copyright: © Copyright 2001 American Mathematical Society