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Tate, John

Relations between \(K_2\) and Galois cohomology. (English) Zbl 0359.12011

Invent. Math. 36, 257-274 (1976).
Reviewer: Lawrence G. Roberts
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Cited in 10 Reviews
Cited in 208 Documents

MSC:

11R70 \(K\)-theory of global fields
11R34 Galois cohomology
12G05 Galois cohomology
19F15 Symbols and arithmetic (\(K\)-theoretic aspects)
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\textit{J. Tate}, Invent. Math. 36, 257--274 (1976; Zbl 0359.12011)
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References:

[1] Bass, H.:K 2 of global fields. AMS taped lecture, Cambridge, Mass., Oct. 1969
[2] Bass, H.:K 2 des corps, globaux. Seminaire Bourbaki, no. 394, Juin 1971
[3] Bass, H., Tate, J.: The Milnor ring of a global field. In: AlgebraicK-Theory II. Lecture Notes in Math. no. 342. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0299.12013
[4] Candiotti, A.: Computations of Iwasawa invariants andK 2. Compositio Math.29, 89-111 (1974) · Zbl 0364.12003
[5] Candiotti, A., Kramer, K.: OnK 2 and Z1-extensions of number fields (preprint) · Zbl 0388.12004
[6] Carroll, J.: On a relationship between the 2-primary part of the tame kernel and Z2-extensions for complex quadratic fields (preprint)
[7] Cassels, J.W.S., Fröhlich, A.: Algebraic number theory. London-New York: Academic Press 1967 · Zbl 0153.07403
[8] Chase, S.U., Waterhouse, W.C.: Moore’s theorem on uniqueness of reciprocity laws. Inventiones math.16, 267-270 (1972) · Zbl 0245.12009
[9] Coates, J.: OnK 2 and some classical conjectures in algebraic number theory. Annals of Math.95, 99-116 (1972) · Zbl 0245.12005
[10] Coates, J., Lichtenbaum, S.: Onl-adic zeta functions. Annals of Math.98, 498-550 (1973) · Zbl 0279.12005
[11] Elman, R., Lam, T.Y.: On the quaternion symbol homomorphism gf:k 2 F?B(F). In: AlgebraicK-theory II. Lecture Notes in Math.342, 447-463 (1973) Berlin-Heidelberg-New York: Springer 1973
[12] Garland, H.: A finiteness theorem forK 2 of a number field. Annals of Math.94, 534-548 (1971) · Zbl 0247.12103
[13] Iwasawa, K.: OnZ 1 -extensions of algebraic number fields. Annals of Math.98, 246-326 (1973) · Zbl 0285.12008
[14] Lichtenbaum, S.: On the values of zeta andL-functions: I Annals of Math.96, 338-360 (1972) · Zbl 0251.12002
[15] Lichtenbaum, S.: Values of zeta-functions, étale cohomology, and algebraicK-theory In: AlgebraicK-theory II. Lecture Notes in Math.342, 489-501. Berlin-Heidelberg-New York: Springer 1973
[16] Milnor, J.: AlgebraicK-theory and quadratic forms. Inventiones math9, 318-344 (1970) · Zbl 0199.55501
[17] Milnor, J.: Introduction to algebraicK-theory. Annals of Math. Study 72. Princeton: Princeton University Press 1971 · Zbl 0237.18005
[18] Moore, C.: Group extensions ofp-adic and adelic linear groups. Publ. Math. I.H.E.S.,35, 5-74, (1969)
[19] Quillen, D.: Higher algebraicK-theory I. In: AlgebraicK-Theory I. Lecture Notes in Math.341, 85-147. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0292.18004
[20] Quillen, D.: Finite generation of the groupsK i of algebraic integers. In: AlgebraicK-theory I. Lecture Notes in Math.341, 179-198, Berlin-Heidelberg-New York: Springer
[21] Serre, J.-P.: Corps locaux, 2 d Éd. Paris: Hermann 1968
[22] Serre, J.-P.: Cohomologie Galoisienne. Lecture Notes in Math.5, Berlin-Heidelberg-New York: Springer 1964 · Zbl 0143.05901
[23] Serre, J.-P.: A Course in arithmetic. Graduate Text in Math.7 (Cours d’Arithmetique), Paris: Press. Univ. de France. 1970). Berlin-Heidelberg-New York: Springer 1973
[24] Tate, J.: Symbols in arithmetic. Actes. Congrès intern. math. 1970, Tome 1, p. 201 a 211.
[25] Tate, J.: Letter to Iwasawa. In: AlgebraicK-theory II. Lecture Notes in Math.342, 524-527 Berlin-Heidelberg-New York: Springer 1973
[26] Weil, A.: Basic number theory. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0267.12001
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