Motivic cohomology with 𝐙/2-coefficients
Publications Mathématiques de l'IHÉS, Tome 98 (2003), pp. 59-104 
@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 = {https://www.numdam.org/articles/10.1007/s10240-003-0010-6/}
}
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Voevodsky, Vladimir. Motivic cohomology with $\mathbf {Z}/2$-coefficients. Publications Mathématiques de l'IHÉS, Tome 98 (2003), pp. 59-104. doi: 10.1007/s10240-003-0010-6

1. 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. | Zbl | MR

2. A. Beilinson, Height pairing between algebraic cycles, In K-theory, Arithmetic and Geometry, Lecture Notes in Math. 1289 (1987), pp. 1-26, Springer. | Zbl | MR

3. S. Bloch, Lectures on algebraic cycles, Duke Univ. Press, 1980. | Zbl | MR

4. S. Bloch and S. Lichtenbaum, A spectral sequence for motivic cohomology, www.math.uiuc.edu/K-theory/062, 1994.

5. S. Borghesi, Algebraic Morava K-theories, Invent. Math., 151 (2) (2003), 381-413. | Zbl | MR

6. 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. | Zbl | MR | Numdam

7. T. Geisser and M. Levine, The K-theory of fields in characteristic p, Invent. Math., 139 (3) (2000), 459-493. | Zbl | MR

8. T. Geisser and M. Levine, The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky, J. Reine Angew. Math., 530 (2001), 55-103. | Zbl | MR

9. R. Hartshorne, Algebraic Geometry, Heidelberg: Springer, 1971. | Zbl | MR

10. J.-P. Jouanolou, Une suite exacte de Mayer-Vietoris en K-theorie algebrique, Lecture Notes in Math. 341 (1973), pp. 293-317. | Zbl | MR

11. B. Kahn, La conjecture de Milnor (d'après V. Voevodsky), Astérisque, (245): Exp. No. 834, 5 (1997), 379-418. Séminaire Bourbaki, Vol. 1996/97. | Zbl | Numdam

12. N. Karpenko, Characterization of minimal Pfister neighbors via Rost projectors, J. Pure Appl. Algebra, 160 (2001), 195-227. | Zbl | MR

13. K. Kato, A generalization of local class field theory by using K-groups, II, J. Fac. Sci., Univ Tokyo, 27 (1980), 603-683. | Zbl | MR

14. T. Y. Lam, The algebraic theory of quadratic forms, Reading, MA: The Benjamin/Cummings Publ., 1973. | Zbl | MR

15. S. Lichtenbaum, Values of zeta-functions at non-negative integers, In Number theory, Lecture Notes in Math. 1068 (1983), pp. 127-138, Springer. | Zbl | MR

16. H. R. Margolis, Spectra and Steenrod algebra, North-Holland, 1983. | Zbl | MR

17. V. Voevodsky, C. Mazza and C. Weibel, Lectures on motivic cohomology, I, www.math.uiuc.edu/K-theory/486, 2002.

18. A. Merkurjev, On the norm residue symbol of degree 2, Sov. Math. Dokl., (1981), 546-551. | Zbl

19. A. Merkurjev and A. Suslin, K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Math. USSR Izvestiya, 21 (1983), 307-340. | Zbl

20. A. Merkurjev and A. Suslin, The norm residue homomorphism of degree three, Math. USSR Izvestiya, 36(2) (1991), 349-367. | Zbl | MR

21. J. Milnor, Algebraic K-theory and quadratic forms, Invent. Math., 9 (1970), 318-344. | Zbl | MR

22. J. Milnor, Introduction to Algebraic K-theory, Princeton, N.J.: Princeton Univ. Press, 1971. | Zbl | MR

23. F. Morel and V. Voevodsky, A 1-homotopy theory of schemes, Publ. Math. IHES, (90) (1999), 45-143. | Zbl | MR | Numdam

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. | Zbl | MR

25. 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. | Zbl

26. D. C. Ravenel, Nilpotence and periodicity in stable homotopy theory, Ann. of Math. Studies 128. Princeton, 1992. | Zbl | MR

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. A. Suslin, Algebraic K-theory and the norm residue homomorphism, J. Soviet Math., 30 (1985), 2556-2611. | Zbl | MR

32. A. Suslin, Higher Chow groups and etale cohomology, In Cycles, transfers and motivic homology theories, pp. 239-254, Princeton: Princeton Univ. Press, 2000. | Zbl | MR

33. 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. | Zbl | MR

34. J. Tate, Relations between K2 and Galois cohomology, Invent. Math., 36 (1976), 257-274. | Zbl | MR

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. | Zbl | MR

38. 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. | Zbl | MR

39. 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. | Zbl | MR

40. V. Voevodsky, Lectures on motivic cohomology 2000/2001 (written by Pierre Deligne), www.math.uiuc.edu/ K-theory /527, 2000/2001.

41. V. Voevodsky, Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic, Int. Math. Res. Not., (7) (2002), 351-355. | Zbl | MR

42. V. Voevodsky, Reduced power operations in motivic cohomology, Publ. Math. IHES (this volume), 2003. | Zbl | MR | Numdam

43. V. Voevodsky, E. M. Friedlander and A. Suslin, Cycles, transfers and motivic homology theories, Princeton: Princeton University Press, 2000. | Zbl | MR

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