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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. Beilinson, Higher Regulators and Values of $L$-functions, Itogi Nauki i Tekhniki 24 (1984), 181-238 (Russian); transl. J. Soviet Mathematics 30 (1985), 2036-2070. MR 86h:11103
  • [Be2] A. Beilinson, Notes on Absolute Hodge Cohomology, Contemp. Math., vol. 55 (Part I), AMS, 1986, pp. 35-68. MR 87m:14019
  • [Be3] A. Beilinson, Letter to Soulé, 1/11/1982.
  • [Be4] A. Beilinson, Height pairing between algebraic cycles, Lecture Notes in Math., vol. 1289, Springer-Verlag, 1987, pp. 1-25. MR 89h:11027
  • [Bl] S. Bloch, Algebaic cycles and higher $K$-theory, Adv. Math. 61 (1986), 267-304. MR 88f:18010
  • [D] P. Deligne, Théorie de Hodge II et III, Publ. Math. IHES 40 (1972), 5-57; 44 (1974), 5-77. MR 58:16653a; MR 58:16653b
  • [Dz] M. Demazure, Motifs de varietés algébriques, Sem. Bourbaki, vol. 365, 1969.
  • [FL] E. M. Friedlander and B. Lawson, Moving algebraic cycles of bounded degree, Invent. Math. 132 (1998), 91-119. MR 99k:14011
  • [Fr] P.J. Freyd, Abelian categories, Harper and Row, 1964. MR 29:3517
  • [G57] A. Grothendieck, Classes de Faisceaux et Théorème de Riemann-Roch, Lecture Notes in Math., vol. 225, Springer-Verlag, 1971, pp. 20-77. MR 50:7133
  • [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 - Bombay Colloquium, Oxford Univ. Press, 1969, pp. 193-199. MR 42:3088
  • [G73] A. Grothendieck, Letter to Ilusie, dated May 3, 1973, Appendix to [J1].
  • [H] M. Hanamura, Mixed motives and algebraic cycles, I. Math. Res. Lett. 2 (1995), 811-821. MR 97d:14014
  • [J1] U. Jannsen, Motivic Sheaves and Filtrations on Chow Groups, Motives, Proc. Symp. Pure Math., vol. 55, AMS, 1994, pp. 245-302. MR 95c:14006
  • [J2] U. Jannsen, Motives, numerical equivalence, and semi-simplicity, Inventiones Math. 107 (1992), 447-452. MR 93g:14009
  • [Le] M. Levine, Mixed Motives, AMS, 1998. MR 99i:14025
  • [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] S. Kleiman, Motives, Algebraic Geometry, Oslo 1970 (F. Oort, ed.), Wolters-Noordhoff, 1972, pp. 53-82. MR 52:3152
  • [M] Motives (U. Jannsen, S. Kleiman and J.-P. Serre, eds.), Proc. Symp. Pure Math., vol. 55, AMS, 1994. MR 94i:11004
  • [Ma] Ju. I. Manin, Correspondences, Motifs and Monoidal Transformations, Math. Sbornik AMS Transl. 6 (1968), 439-470 (Russian). MR 41:3482
  • [Q] D. Quillen, Higher algebraic $K$-theory: I, Lecture Notes in Math., vol. 341, Springer-Verlag, 1973, pp. 85-147. MR 49:2895
  • [S] J.-P. Serre, Motifs, Journées Arithmétiques de Luminy (1989) (G. Lachaud, ed.), Astérisque, vol. 198-200, Soc. Math. France, 1991, pp. 333-349. MR 92m:14002
  • [Sh] Richard Shiff, Sensation, movement, Cezanne, Classic Cezanne (Terence Maloon, ed.), Sydney, 1998, pp. 13-27.
  • [SV] A. Suslin and V. Voevodsky, Bloch-Kato conjecture and motivic cohomology with finite coefficients, The Arithmetic and Geometry of Algebraic Cycles, NATO Science Series C, vol. 548, Kluwer, 2000, pp. 117-189. MR 2001g:14031
  • [V] V. Voevodsky, The Milnor Conjecture, preprint (1996), 0170.

Review Information:

Reviewer: Charles A. Weibel
Affiliation: Rutgers University
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
American Mathematical Society