Duality theorems for Γ-extensions of algebraic number fields
Compositio Mathematica, Tome 55 (1985) no. 3, p. 333-381
@article{CM_1985__55_3_333_0,
     author = {Wingberg, Kay},
     title = {Duality theorems for $\Gamma $-extensions of algebraic number fields},
     journal = {Compositio Mathematica},
     publisher = {Martinus Nijhoff Publishers},
     volume = {55},
     number = {3},
     year = {1985},
     pages = {333-381},
     zbl = {0608.12012},
     language = {en},
     url = {http://www.numdam.org/item/CM_1985__55_3_333_0}
}
Wingberg, Kay. Duality theorems for $\Gamma $-extensions of algebraic number fields. Compositio Mathematica, Tome 55 (1985) no. 3, pp. 333-381. http://www.numdam.org/item/CM_1985__55_3_333_0/

[1] N. Bourbaki: Algebre commutative. Paris: Herman (1969).

[2] J. Coates: On K2 and some classical conjectures in algebraic number theory. Ann. of math. 95 (1972) 99-116. | MR 360523 | Zbl 0245.12005

[3] J. Coates: K - theory and Iwasawa's analogue of the Jacobian. Algebraic K-Theory, II (Seattle 1972). Springer Lecture notes in maths. 342 (1973) 502-520. | MR 406977 | Zbl 0284.12006

[4] J. Coates, S. Lichtenbaum, S. On l-adic zeta functions. Ann. of Math. 98 (1973) 498-550. | MR 330107 | Zbl 0279.12005

[5] R. Greenberg, On the Iwasawa invariants of totally real number fields. Amer. J. math. 98 (1976) 263-284. | MR 401702 | Zbl 0334.12013

[6] R. Greenberg, On the structure of certain Galois groups. Invent math. 47 (1978) 85-99. | MR 504453 | Zbl 0403.12004

[7] K. Grunberg, Cohomological topics in group theory. Springer Lecture notes in maths. 143 (1970). | MR 279200 | Zbl 0205.32701

[8] K. Haberland, Galois cohomology of algebraic number fields. Berlin: Deutscher Verlag der Wissenschaften (1978). | MR 519872 | Zbl 0418.12004

[9] K. Iwasawa, On Z l-extensions of algebraic number fields. Ann. of math. 98 (1973) 246-326. | MR 349627 | Zbl 0285.12008

[10] K. Iwasawa, On the μ-invariants of Z l-extensions. Number theory, algebraic geometry and commutative algebra (in honor of Y. Akizuki). Kinokuniya. Tokyo (1973) 1-11. | Zbl 0281.12005

[11] K. Iwasawa, Riemann-Hurwitz formula and p-adic Galois representations for number fields. Tôhoku Math. J. 33 (1981) 263-288. | MR 624610 | Zbl 0468.12004

[12] A.V. Jakovlev, The Galois group of the algebraic closure of a local field. Math. USSR - Izv. 2 (1968) 1231-1269. | MR 236155 | Zbl 0194.35401

[13] U. Jannsen, Über die Galoismodulstruktur und die absolute Galoisgruppe p-adischer Zahlkörper. Dissertation. Hamburg (1980). | Zbl 0535.12012

[14 U. Jannsen, Über Galoisgruppen lokaler Körper. Invent. math. 70 (1982) 53-69. | MR 679773 | Zbl 0534.12009

[15] U. Jannsen; K. Wingberg, Die p-Vervollständigung der multiplikativen Gruppe einer p-Erweiterung eines irregulären p-adischen Zahlkörpers. J. für reine angew. Math. 307/308, (1979) 399-410. | MR 534234 | Zbl 0396.12015

[16] Y. Kida, l-extensions of CM-fields and cyclotomic invariants. J. Number theory 12 (1980) 519-528. | MR 599821 | Zbl 0455.12007

[17] L. Kuz'Min, Some duality theorems for cyclotomic Γ-extensions over algebraic number fields of CM-type Math. USSR-Izv. 14 (1980) 441-498. | Zbl 0448.12007

[18] S. Lang. Cyclotomic fields. Graduate texts in maths. New York-Heidelberg- Berlin: Springer (1978). | MR 485768 | Zbl 0395.12005

[19] T. Nakayama, On modules of trivial cohomology over a finite group. Illinois J. Math. 1 (1957) 36-43. | MR 84014 | Zbl 0207.33601

[20] O. Neumann, On p-closed number fields and an analogue of Riemann's existence theorem. In: A. Pröhlich (ed.) "Algebraic number fields ". London: Acad. press (1977) 625-647. | MR 453698 | Zbl 0393.12015

[21] P. Schneider, Über gewisse Galoiscohomologiegruppen. Math. Zeitschrift 168 (1979) 181-205. | MR 544704 | Zbl 0421.12024

[22] P. Schneider, Die Galoiscohomologie p-adischer Darstellungen über Zahlkörpern. Dissertation. Regensburg (1980).

[23] J-P. Serre, Cohomologie galoisienne. Lecture notes in maths. 5 (1964). | MR 201444 | Zbl 0136.02801

[24] R.G. Swan, Induced representaions and projectives modules. Ann. of Math. 71 (1960) 552-579. | MR 138688 | Zbl 0104.25102

[25] K. Wingberg, Freie Produktzerlegungen von Galoisgruppen und Iwasawa-Invarianten für p-Erweiterungen von Q. J. für reine und angewandte Math. 341 (1983) 111-129. | MR 697311 | Zbl 0501.12014

[26] J.P. Wintenberger, Structure galoisienne de limites projectives d'unités loales. Compos. Math. 42 (1980) 89-104. | Numdam | MR 594484 | Zbl 0414.12008