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Local Fields


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One Local Fields (Basic Facts).- I Discrete Valuation Rings and Dedekind Domains.- II Completion.- Two Ramification.- III Discriminant and Different.- IV Ramification Groups.- V The Norm.- VI Artin Representation.- Three Group Cohomology.- VII Basic Facts.- VIII Cohomology of Finite Groups.- IX Theorems of Tate and Nakayama.- X Galois Cohomology.- XI Class Formations.- Four Local Class Field Theory.- XII Brauer Group of a Local Field.- XIII Local Class Field Theory.- XIV Local Symbols and Existence Theorem.- XV Ramification.- Supplementary Bibliography for the English Edition.

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