@article{PMIHES_2003__98__59_0, author = {Voevodsky, Vladimir}, title = {Motivic cohomology with $\mathbf {Z}/2$-coefficients}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {59--104}, publisher = {Springer}, volume = {98}, year = {2003}, doi = {10.1007/s10240-003-0010-6}, zbl = {1057.14028}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-003-0010-6/} }
TY - JOUR AU - Voevodsky, Vladimir TI - Motivic cohomology with $\mathbf {Z}/2$-coefficients JO - Publications Mathématiques de l'IHÉS PY - 2003 SP - 59 EP - 104 VL - 98 PB - Springer UR - http://www.numdam.org/articles/10.1007/s10240-003-0010-6/ DO - 10.1007/s10240-003-0010-6 LA - en ID - PMIHES_2003__98__59_0 ER -
Voevodsky, Vladimir. Motivic cohomology with $\mathbf {Z}/2$-coefficients. Publications Mathématiques de l'IHÉS, Volume 98 (2003), pp. 59-104. doi : 10.1007/s10240-003-0010-6. http://www.numdam.org/articles/10.1007/s10240-003-0010-6/
1. The Milnor ring of a global field, In K-theory II, Lecture Notes in Math. 342 (1973), pp. 349-446, Springer. | MR | Zbl
and ,2. Height pairing between algebraic cycles, In K-theory, Arithmetic and Geometry, Lecture Notes in Math. 1289 (1987), pp. 1-26, Springer. | MR | Zbl
,3. Lectures on algebraic cycles, Duke Univ. Press, 1980. | MR | Zbl
,4. S. Bloch and S. Lichtenbaum, A spectral sequence for motivic cohomology, www.math.uiuc.edu/K-theory/062, 1994.
5. Algebraic Morava K-theories, Invent. Math., 151 (2) (2003), 381-413. | MR | Zbl
,6. The spectral sequence relating algebraic K-theory to motivic cohomology, Ann. Sci. École Norm. Sup. (4), 35 (6) (2002), 773-875. | Numdam | MR | Zbl
and ,7. The K-theory of fields in characteristic p, Invent. Math., 139 (3) (2000), 459-493. | MR | Zbl
and ,8. The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky, J. Reine Angew. Math., 530 (2001), 55-103. | MR | Zbl
and ,9. Algebraic Geometry, Heidelberg: Springer, 1971. | MR | Zbl
,10. Une suite exacte de Mayer-Vietoris en K-theorie algebrique, Lecture Notes in Math. 341 (1973), pp. 293-317. | MR | Zbl
,11. La conjecture de Milnor (d'après V. Voevodsky), Astérisque, (245): Exp. No. 834, 5 (1997), 379-418. Séminaire Bourbaki, Vol. 1996/97. | Numdam | Zbl
,12. Characterization of minimal Pfister neighbors via Rost projectors, J. Pure Appl. Algebra, 160 (2001), 195-227. | MR | Zbl
,13. A generalization of local class field theory by using K-groups, II, J. Fac. Sci., Univ Tokyo, 27 (1980), 603-683. | MR | Zbl
,14. The algebraic theory of quadratic forms, Reading, MA: The Benjamin/Cummings Publ., 1973. | MR | Zbl
,15. Values of zeta-functions at non-negative integers, In Number theory, Lecture Notes in Math. 1068 (1983), pp. 127-138, Springer. | MR | Zbl
,16. Spectra and Steenrod algebra, North-Holland, 1983. | MR | Zbl
,17. V. Voevodsky, C. Mazza and C. Weibel, Lectures on motivic cohomology, I, www.math.uiuc.edu/K-theory/486, 2002.
18. On the norm residue symbol of degree 2, Sov. Math. Dokl., (1981), 546-551. | Zbl
,19. K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Math. USSR Izvestiya, 21 (1983), 307-340. | Zbl
and ,20. The norm residue homomorphism of degree three, Math. USSR Izvestiya, 36(2) (1991), 349-367. | MR | Zbl
and ,21. Algebraic K-theory and quadratic forms, Invent. Math., 9 (1970), 318-344. | MR | Zbl
,22. Introduction to Algebraic K-theory, Princeton, N.J.: Princeton Univ. Press, 1971. | MR | Zbl
,23. homotopy theory of schemes, Publ. Math. IHES, (90) (1999), 45-143. | Numdam | MR | Zbl
and , A 1-24. 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. | MR | Zbl
25. An exact sequence for Milnor's K-theory with applications to quadratic forms, www.math.uiuc.edu/K-theory/0454, 2000. | Zbl
, and ,26. Nilpotence and periodicity in stable homotopy theory, Ann. of Math. Studies 128. Princeton, 1992. | MR | Zbl
,27. M. Rost, Hilbert 90 for K3 for degree-two extensions, www.math.ohio-state.edu/∼rost/K3-86.html, 1986.
28. M. Rost, On the spinor norm and A0(X, K1) for quadrics, www.math.ohio-state.edu/∼rost/spinor.html, 1988.
29. M. Rost, Some new results on the Chowgroups of quadrics, www.math.ohio-state.edu/∼rost/chowqudr.html, 1990.
30. M. Rost, The motive of a Pfister form, www.math.ohio-state.edu/∼rost/motive.html, 1998.
31. Algebraic K-theory and the norm residue homomorphism, J. Soviet Math., 30 (1985), 2556-2611. | MR | Zbl
,32. Higher Chow groups and etale cohomology, In Cycles, transfers and motivic homology theories, pp. 239-254, Princeton: Princeton Univ. Press, 2000. | MR | Zbl
,33. Bloch-Kato conjecture and motivic cohomology with finite coefficients, In The arithmetic and geometry of algebraic cycles, pp. 117-189, Kluwer, 2000. | MR | Zbl
and ,34. Relations between K2 and Galois cohomology, Invent. Math., 36 (1976), 257-274. | MR | Zbl
,35. V. Voevodsky, Bloch-Kato conjecture for Z/2-coefficients and algebraic Morava K-theories, www.math.uiuc.edu/K-theory/76, 1995.
36. V. Voevodsky, The Milnor Conjecture, www.math.uiuc.edu/K-theory/170, 1996.
37. V. Voevodsky, The A 1-homotopy theory, In Proceedings of the international congress of mathematicians, 1 (1998), pp. 579-604, Berlin. | MR | Zbl
38. 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. | MR | Zbl
,39. 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. | MR | Zbl
,40. V. Voevodsky, Lectures on motivic cohomology 2000/2001 (written by Pierre Deligne), www.math.uiuc.edu/ K-theory /527, 2000/2001.
41. Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic, Int. Math. Res. Not., (7) (2002), 351-355. | MR | Zbl
,42. Reduced power operations in motivic cohomology, Publ. Math. IHES (this volume), 2003. | Numdam | MR | Zbl
,43. Cycles, transfers and motivic homology theories, Princeton: Princeton University Press, 2000. | MR | Zbl
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