Colliot-Thelene, Jean-Louis Hilbert’s theorem 90 for \(K^ 2\), with application to the Chow groups of rational surfaces. (English) Zbl 0527.14011 Invent. Math. 71, 1-20 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 47 Documents 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 Keywords:Chow groups; group of zero-dimensional cycles; rational equivalence; rational surface; K-theoretic methods; finiteness theorems; rational point; good reduction; geometrically integral variety; vanishing theorem × Cite Format Result Cite Review PDF Full Text: DOI EuDML 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 · doi:10.1090/S0002-9904-1974-13587-1 [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 · doi:10.1016/0021-8693(78)90277-6 [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 · doi:10.1215/S0012-7094-81-04824-9 [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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.