## Hilbert’s theorem 90 for $$K^ 2$$, with application to the Chow groups of rational surfaces.(English)Zbl 0527.14011

### MSC:

 14C35 Applications of methods of algebraic $$K$$-theory in algebraic geometry 14C15 (Equivariant) Chow groups and rings; motives 14M20 Rational and unirational varieties 14C25 Algebraic cycles 14C05 Parametrization (Chow and Hilbert schemes) 14G05 Rational points 14J25 Special surfaces
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### References:

 [1] Bass, H., Tate, J.: The Milnor ring of a global field, AlgebraicK-Theory II. Lecture notes in math., vol. 342, pp. 349-446. Berlin-Heidelberg-New York: Springer 1973 [2] Bloch, S.: Torsion algebraic cycles,K 2 and Brauer groups of function fields. Bull. A.M.S.80, 941-945 (1974); expanded in Groupe de Brauer, éd. Kervaire, M., et Ojanguren, M. Lecture notes in math., vol. 844, pp. 75-102. Berlin-Heidelberg-New York: Springer 1981 · Zbl 0289.14002 [3] Bloch, S.: Lectures on algebraic cycles. Duke University Lecture Notes in Mathematics no 4 1980 · Zbl 0436.14003 [4] Bloch, S.: On the Chow groups of certain rational surfaces. Ann. Sc. E.N.S.14, 41-59 (1981) · Zbl 0524.14006 [5] Bloch, S.: Letter to C. Soulé (November 1981) [6] Bloch, S.: The dilogarithm and extensions of Lie algebras. AlgebraicK-Theory, Evanston (Friedlander, E.M., Stein, M.R., eds.) Lecture notes in math., vol. 854, pp. 1-23. Berlin-Heidelberg-New York: Springer 1981 [7] Bloch, S.: Some formulas pertaining to theK-theory of commutative group schemes. Journal of Algebra53, 304-326 (1978) · Zbl 0432.14014 [8] Colliot-Thélène, J.-L., Ischebeck, F.: L’équivalence rationnelle sur les cycles de dimension zéro des variétés algébriques réelles, C.R. Acad. Sc. Paris292, 723-725 (1981) · Zbl 0472.14016 [9] Colliot-Thélène, J.-L., Sansuc, J.-J.: On the Chow groups of certain rational surfaces: a sequel to a paper of S. Bloch. Duke Math. Journal48, 421-447 (1981) · Zbl 0479.14006 [10] Colliot-Thélène, J.-L., Sansuc, J.-J.: Quelques gammes sur les formes quadratiques (to appear in the Journal of Algebra) · Zbl 0515.10018 [11] Colliot-Thélène, J.-L., Sansuc, J.-J., Soulé, C.: Quelques théorèmes de finitude en théorie des cycles algébriques. C.R. Acad. Sc. Paris294, 749-752 (1982) · Zbl 0572.14005 [12] Coray, D.: An argument of Spencer Bloch, typescript (1980) [13] Jouanolou, J.-P.: Théorèmes de Bertini et applications. I.R.M.A., Strasbourg 1979 [14] Kato, K.: A generalization of local class field theory by usingK-groups II. Journal of the Fac. of Sc., The Univ. of Tokyo, Sec. IA27, 603-683 (1980) · Zbl 0463.12006 [15] Lam, T.-Y.: The algebraic theory of quadratic forms. Benjamin, Reading, 1973 · Zbl 0259.10019 [16] Merkur’ev, A.S., Suslin, A.A.:K-cohomology of Severi-Brauer varieties and norm residue homomorphism, Izvestija Akad. Nauk SSSR Ser. Mat. Tom 46, no 5 (1982), 1011-1046 [17] Milnor, J.: Introduction to algebraicK-theory, Annals of Mathematics Studies, Princeton University Press, no 72, 1971 · Zbl 0237.18005 [18] Suslin, A.A.: Torsion inK 2 of fields (preprint)
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