• Jean-Pierre Serre
Part of the Graduate Texts in Mathematics book series (GTM, volume 67)


The goal of this book is to present local class field theory from the cohomological point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions—primarily abelian—of “local” (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of “localisation”.


Valuation Ring Residue Field Discrete Valuation Ring Dedekind Domain Completion Process 
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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Collège de FranceParisFrance

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