International Congress of Mathematicians

84 Markus RostFor n = 2 one can take here the Severi-Brauer varieties and for n = 3 theMerkurjev-Suslin varieties. Hence we have:Corollary. Suppose charfc = 0. Then Hilbert's 90 holds for symbols ofweight < 3.References[i[2:[3;[4;[*.[6;[r[8[9[io;[n[12:[is;[w:[15[16D. Abramovich, K. Karu, K. Matsuki, and J. Wlodarczyk, Tarification andfactorization of birational maps, J. Amer. Math. Soc. 15 (2002), no. 3, 531^572 (electronic).E. Bierstone and P. D. Milman, Canonical desingularization in characteristiczero by blowing up the maximum strata of a local invariant, Invent. Math. 128(1997), no. 2, 207^302.S. Borghesi, Algebraic Morava K-theories and the higher degree formula, thesis,2000, Evanston, http://www.math.uiuc.edu/K-theory/0412S. Buoncristiano and D. Hacon, The geometry of Chern numbers, Ann. of Math.(2) 118 (1983), no. 1, 1-7.P. E. Conner and E. E. Floyd, Differentiable periodic maps, Academic PressInc., Publishers, New York, 1964, Ergebnisse der Mathematik und ihrer Grenzgebiete,N. F., Band 33.P. K. Draxl, Skew fields, London Mathematical Society Lecture Note Series,vol. 81, Cambridge University Press, Cambridge, 1983.E. E. Floyd, Actions of (Z p ) k without stationary points, Topology 10 (1971),327^336.B. Kahn, La conjecture de Milnor (d'après V. Voevodsky), Astérisque (1997),no. 245, Exp. No. 834, 5, 379^418, Séminaire Bourbaki, Vol. 1996/97.T. Y. Lam, The algebraic theory of quadratic forms, Benjamin/Cummings PublishingCo. Inc. Advanced Book Program, Reading, Mass., 1980, Revised secondprinting, Mathematics Lecture Note Series.M. Levine and F. Morel, Algebraic cobordism I, preprint, 2002,http://www.math.uiuc.edu/K-theory/0547A. S. Merkurjev, Degree formula, notes, May 2000,http://www.math.ohio-state.edu/~rost/chain-lemma.htmlA. S. Merkurjev and A. A. Suslin, K-cohomology of Severi-Brauer varietiesand the norm residue homomorphism, Izv. Akad. Nauk SSSR Ser. Mat. 46(1982), no. 5, 1011-1046, 1135-1136 (Russian), [Math. USSR Izv. 21 (1983),307-340]., The group of K\ -zero-cycles on Severi-Brauer varieties, Nova J. AlgebraGeom. 1 (1992), no. 3, 297^315., Norm residue homomorphism of degree three, Izv. Akad. Nauk SSSRSer. Mat. 54 (1990), no. 2, 339^356 (Russian), [Math. USSR Izv. 36 (1991),no. 2, 349-367], also: LOMI-preprint (1986).J. Milnor, Algebraic K-theory and quadratic forms, Invent. Math. 9 (1970),318^344.D. Quillen, Elementary proofs of some results of cobordism theory using Steen-