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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
[Be1] A. Beilinson, Higher Regulators and Values of 
-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 
-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 
-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), www.math.uiuc.edu/K-theory/ 0170.
- [Be1]
- A. Beilinson, Higher Regulators and Values of -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 -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 -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), 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
Published electronically:
October 12, 2001
Additional Notes:
Weibel was partially supported by NSF grant DMS98-01560
Review copyright:
© Copyright 2001
American Mathematical Society
