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Schneider, Peter

Über gewisse Galoiscohomologiegruppen. (German) Zbl 0421.12024

Math. Z. 168, 181-205 (1979).
Reviewer: Loren D. Olson (Tromsø)
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scan of Zbl 0421.12024

Cited in 9 Reviews
Cited in 71 Documents

MSC:

12G05 Galois cohomology
11R34 Galois cohomology
11R42 Zeta functions and \(L\)-functions of number fields
11S25 Galois cohomology

Keywords:

Galois cohomology groups; Dedekind zeta-function; Lichtenbaum conjecture; Tate-Poitou duality
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Full Text: DOI EuDML

References:

[1] Artin, E., Tate, J.: Class field theory. New York-Amsterdam: Benjamin 1968 · Zbl 0176.33504
[2] Birch, B.:K 2 of global fields. In: Institute on Number Theory. Proc. Symp. Pure Math. XX (New York 1969), pp. 87-95. Providence: American Mathematical Society 1971
[3] Brumer, A.: On the units of algebraic number fields. Mathematika14, 121-124 (1967) · Zbl 0171.01105 · doi:10.1112/S0025579300003703
[4] Coates, J.: OnK 2 and some classical conjectures in algebraic number theory. Ann. of Math.95, 99-116 (1972) · Zbl 0245.12005 · doi:10.2307/1970857
[5] Coates, J.:p-adicL-functions and Iwasawa’s theory. In: Fröhlich, Algebraic Number Fields. Proceedings of a Symposium (Durham 1975), pp. 269-353. New York-London: Academic Press 1977
[6] Garland, H.: A finiteness theorem forK 2 of a number field. Ann. of Math.94, 534-548 (1971) · Zbl 0247.12103 · doi:10.2307/1970769
[7] Greenberg, R.: Onp-adicL-functions and cyclotomic fields. Nagoya Math. J.56, 61-77 (1974)
[8] Haberland, K.: Zu Tate’s Dualitätssatz in der Galois-Cohomologie über Zahlkörpern. Dissertation, Berlin 1975
[9] Iwasawa, K.: On ? t of algebraic number fields. Ann. of Math.98, 246-326 (1973) · Zbl 0285.12008 · doi:10.2307/1970784
[10] Kaplansky, I.: Infinite Abelian Groups. Ann Arbor: University of Michigan Press 1969 · Zbl 0194.04402
[11] Koch, H.: Galoissche Theorie derp-Erweiterungen. Berlin: Deutscher Verlag der Wissenschaften 1970
[12] Kubota, T.: Galois group of the maximal Abelian extension over an algebraic number field. Nagoya Math. J.12, 177-189 (1957) · Zbl 0079.26803
[13] Kuz’min, L.V.: The Tate module for algebraic number fields. Izw. Akad. Nauk SSSR Ser. Mat.36, 267-327 (1972) [russ.]; engl. Transl.: Math. USSR-Izv.6, 263-321 (1972)
[14] Lenstra, H.W.:K 2 of a global field consists of symbols. In: AlgebraicK-Theory. Proceedings of a Conference (Evanston 1976), pp. 69-73. Lecture Notes in Mathematics551. Berlin-Heidelberg-New York: Springer 1976
[15] Miki, H.: On the maximal Abelianl-extension of a finite algebraic number field with given ramification. Nagoya Math. J.70, 183-202 (1978) · Zbl 0398.12003
[16] Neukirch, J.: Einbettungsprobleme mit lokaler Vorgabe und freie Produkte lokaler Galoisgruppen. J. Reine Angew. Math.259, 1-47 (1973) · Zbl 0263.12006 · doi:10.1515/crll.1973.259.1
[17] Neukirch, J.: Über das Einbettungsproblem der algebraischen Zahlentheorie. Invent. Math.21, 59-116 (1973) · Zbl 0267.12005 · doi:10.1007/BF01389690
[18] Onabe, M.: On the Isomorphisms of the Galois Groups of the Maximal Abelian Extensions of Imaginary Quadratic Fields. Natur. Sci. Rep. Ochanomizu Univ.27, 155-161 (1976) · Zbl 0354.12004
[19] Serre, J.-P.: Classes des corps cyclotomiques. Séminaire Bourbaki 1958, exp. 174
[20] Serre, J.-P.: Corps locaux. Paris: Hermann 1962 · Zbl 0137.02601
[21] CG. Serre, J.-P.: Cohomologie Galoisienne. Lecture Notes in Mathematics 5. Berlin-Heidelberg-New York: Springer 1973
[22] Takahashi, T.: On Extensions with Given Ramification. Proc. Japan Acad.44, 771-775 (1968) · Zbl 0199.37501 · doi:10.3792/pja/1195521027
[23] Tate, J.: Duality theorems in Galois cohomology over number fields. In: Proceedings of the International Congress of Mathematicans (Stockholm 1962), pp. 288-295. Uppsala: Almquist-Wiksells 1963
[24] Tate, J.: On the conjectures of Birch and Swinnerton-Dyer and a geometric analog. Séminaire Bourbaki 1965/66, exp. 306. New York-Amsterdam: Benjamin 1966
[25] Tate, J.: Symbols in arithmetic. In: Actes du Congrès International des Mathématiciens (Nice 1970) Some1, pp. 201-211. Paris: Gauthier-Villars 1971 · Zbl 0229.12013
[26] Tate, J.: The Milnor ring of a global field. Appendix. In: AlgebraicK-Theory II. Proceedings of a Conference (Seattle 1972), pp. 429-446. Lecture Notes in Mathematics342. Berlin-Heidelberg-New York: Springer 1973
[27] Tate, J.: Letter to Iwasawa. In: AlgebraicK-Theory II. Proceedings of a Conference (Seattle 1972), pp. 524-527. Lecture Notes in Mathematics342. Berlin-Heidelberg-New York: Springer 1973
[28] Tate, J.: Relations betweenK 2 and Galois Cohomology. Invent. Math.36, 257-274 (1976) · Zbl 0359.12011 · doi:10.1007/BF01390012
[29] CL. Coates, J., Lichtenbaum, S.: Onl-adic zeta functions. Ann. of Math.98, 498-550 (1973) · Zbl 0279.12005 · doi:10.2307/1970916
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