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Local class field theory via group cohomology method.

by Au Pat Nien. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 86-88). / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Valuations --- p.4 / Chapter 2.1 --- Preliminaries --- p.4 / Chapter 2.2 --- Complete Fields --- p.6 / Chapter 2.3 --- Unramified Extension of Complete Field --- p.10 / Chapter 2.4 --- Local Fields --- p.12 / Chapter 3 --- Ramification Groups and Hasse-Herbrand Function --- p.16 / Chapter 3.1 --- Ramification Groups --- p.16 / Chapter 3.2 --- "The Quotients Gi/Gi+1, i ≥ 0" --- p.17 / Chapter 3.3 --- The Hasse-Herbrand function --- p.19 / Chapter 4 --- The Norm Map --- p.21 / Chapter 4.1 --- Lemmas --- p.21 / Chapter 4.2 --- The Norm Map on the Residue Field of a Totally Ramified Extension of Prime Degree --- p.22 / Chapter 4.3 --- Extension of the Perfect Residue Field in a Totally Ramified Extension --- p.26 / Chapter 4.4 --- The Norm Map on Finite Separable Extension of Knr with K Perfect --- p.28 / Chapter 5 --- Cohomology of Finite Groups --- p.30 / Chapter 5.1 --- Preliminaries --- p.30 / Chapter 5.2 --- Mappings of Cohomology Groups --- p.32 / Chapter 5.2.1 --- Restriction and Inflation --- p.32 / Chapter 5.2.2 --- Corestriction --- p.34 / Chapter 5.3 --- Cup Product --- p.34 / Chapter 5.4 --- Cohomology Groups of Low Dimensions --- p.35 / Chapter 5.5 --- Some Results of Group Cohomology --- p.43 / Chapter 6 --- The Brauer Group of a Field --- p.57 / Chapter 7 --- The Norm Residue Map --- p.60 / Chapter 7.1 --- Determination of the Brauer Group of a Local Field --- p.60 / Chapter 7.2 --- Canonical Class --- p.62 / Chapter 7.3 --- The Reciprocity Law --- p.64 / Chapter 8 --- The Local Symbol --- p.74 / Chapter 8.1 --- Definition --- p.74 / Chapter 8.2 --- The Hilbert Symbol --- p.74 / Chapter 8.3 --- The Differential of the Formal Power Series --- p.76 / Chapter 8.4 --- The Artin-Schreier Symbol --- p.78 / Chapter 9 --- Characterization of a Norm Group --- p.81 / Bibliography

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_321545
Date January 1996
ContributorsAu, Pat Nien., Chinese University of Hong Kong Graduate School. Division of Mathematics.
PublisherChinese University of Hong Kong
Source SetsThe Chinese University of Hong Kong
LanguageEnglish
Detected LanguageEnglish
TypeText, bibliography
Formatprint, ii, 88 leaves ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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