References
H. Bass and J. Tate, The Milnor ring of a global field, In K-theory II, Lecture Notes in Math. 342 (1973), pp. 349–446, Springer.
A. Beilinson, Height pairing between algebraic cycles, In K-theory, Arithmetic and Geometry, Lecture Notes in Math. 1289 (1987), pp. 1–26, Springer.
S. Bloch, Lectures on algebraic cycles, Duke Univ. Press, 1980.
S. Bloch and S. Lichtenbaum, A spectral sequence for motivic cohomology, www.math.uiuc.edu/K-theory/062, 1994.
S. Borghesi, Algebraic Morava K-theories, Invent. Math., 151 (2) (2003), 381–413.
E. M. Friedlander and A. Suslin, The spectral sequence relating algebraic K-theory to motivic cohomology, Ann. Sci. École Norm. Sup. (4), 35 (6) (2002), 773–875.
T. Geisser and M. Levine, The K-theory of fields in characteristic p, Invent. Math., 139 (3) (2000), 459–493.
T. Geisser and M. Levine, The Bloch-Kato conjecture and a theorem of Suslin–Voevodsky, J. Reine Angew. Math., 530 (2001), 55–103.
R. Hartshorne, Algebraic Geometry, Heidelberg: Springer, 1971.
J.-P. Jouanolou, Une suite exacte de Mayer-Vietoris en K-theorie algebrique, Lecture Notes in Math. 341 (1973), pp. 293–317.
B. Kahn, La conjecture de Milnor (d’après V. Voevodsky), Astérisque, (245): Exp. No. 834, 5 (1997), 379–418. Séminaire Bourbaki, Vol. 1996/97.
N. Karpenko, Characterization of minimal Pfister neighbors via Rost projectors, J. Pure Appl. Algebra, 160 (2001), 195–227.
K. Kato, A generalization of local class field theory by using K-groups, II, J. Fac. Sci., Univ Tokyo, 27 (1980), 603–683.
T. Y. Lam, The algebraic theory of quadratic forms, Reading, MA: The Benjamin/Cummings Publ., 1973.
S. Lichtenbaum, Values of zeta-functions at non-negative integers, In Number theory, Lecture Notes in Math. 1068 (1983), pp. 127–138, Springer.
H. R. Margolis, Spectra and Steenrod algebra, North-Holland, 1983.
V. Voevodsky, C. Mazza and C. Weibel, Lectures on motivic cohomology, I, www.math.uiuc.edu/K-theory/486, 2002.
A. Merkurjev, On the norm residue symbol of degree 2, Sov. Math. Dokl., (1981), 546–551.
A. Merkurjev and A. Suslin, K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Math. USSR Izvestiya, 21 (1983), 307–340.
A. Merkurjev and A. Suslin, The norm residue homomorphism of degree three, Math. USSR Izvestiya, 36(2) (1991), 349–367.
J. Milnor, Algebraic K-theory and quadratic forms, Invent. Math., 9 (1970), 318–344.
J. Milnor, Introduction to Algebraic K-theory, Princeton, N.J.: Princeton Univ. Press, 1971.
F. Morel and V. Voevodsky, A 1-homotopy theory of schemes, Publ. Math. IHES, (90) (1999), 45–143.
Y. Nisnevich, The completely decomposed topology on schemes and associated descent spectral sequences in algebraic K-theory, In Algebraic K-theory: connections with geometry and topology, pp. 241–342, Dordrecht: Kluwer Acad. Publ., 1989.
D. Orlov, A. Vishik and V. Voevodsky, An exact sequence for Milnor’s K-theory with applications to quadratic forms, www.math.uiuc.edu/K-theory/0454, 2000.
D. C. Ravenel, Nilpotence and periodicity in stable homotopy theory, Ann. of Math. Studies 128. Princeton, 1992.
M. Rost, Hilbert 90 for K3 for degree-two extensions, www.math.ohio-state.edu/∼rost/K3-86.html, 1986.
M. Rost, On the spinor norm and A0(X,K1) for quadrics, www.math.ohio-state.edu/∼rost/spinor.html, 1988.
M. Rost, Some new results on the Chowgroups of quadrics, www.math.ohio-state.edu/∼rost/chowqudr.html, 1990.
M. Rost, The motive of a Pfister form, www.math.ohio-state.edu/∼rost/motive.html, 1998.
A. Suslin, Algebraic K-theory and the norm residue homomorphism, J. Soviet Math., 30 (1985), 2556–2611.
A. Suslin, Higher Chow groups and etale cohomology, In Cycles, transfers and motivic homology theories, pp. 239–254, Princeton: Princeton Univ. Press, 2000.
A. Suslin and V. Voevodsky, Bloch-Kato conjecture and motivic cohomology with finite coefficients, In The arithmetic and geometry of algebraic cycles, pp. 117–189, Kluwer, 2000.
J. Tate, Relations between K2 and Galois cohomology, Invent. Math., 36 (1976), 257–274.
V. Voevodsky, Bloch-Kato conjecture for Z/2-coefficients and algebraic Morava K-theories, www.math.uiuc.edu/K-theory/76, 1995.
V. Voevodsky, The Milnor Conjecture, www.math.uiuc.edu/K-theory/170, 1996.
V. Voevodsky, The A 1-homotopy theory, In Proceedings of the international congress of mathematicians, 1 (1998), pp. 579–604, Berlin.
V. Voevodsky, Cohomological theory of presheaves with transfers, In Cycles, transfers and motivic homology theories, Annals of Math Studies, pp. 87–137, Princeton: Princeton Univ. Press, 2000.
V. Voevodsky, Triangulated categories of motives over a field, In Cycles, transfers and motivic homology theories, Annals of Math Studies, pp. 188–238, Princeton: Princeton Univ. Press, 2000.
V. Voevodsky, Lectures on motivic cohomology 2000/2001 (written by Pierre Deligne), www.math.uiuc.edu/ K-theory /527, 2000/2001.
V. Voevodsky, Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic, Int. Math. Res. Not., (7) (2002), 351–355.
V. Voevodsky, Reduced power operations in motivic cohomology, Publ. Math. IHES (this volume), 2003.
V. Voevodsky, E. M. Friedlander and A. Suslin, Cycles, transfers and motivic homology theories, Princeton: Princeton University Press, 2000.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Voevodsky, V. Motivic cohomology with Z/2-coefficients. Publ. Math. 98, 59–104 (2003). https://doi.org/10.1007/s10240-003-0010-6
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10240-003-0010-6