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Friday, August 14, 2020 | History

6 edition of Local class field theory found in the catalog.

Local class field theory

Kenkichi Iwasawa

Local class field theory

by Kenkichi Iwasawa

  • 72 Want to read
  • 33 Currently reading

Published by Oxford University Press, Clarendon Press in New York, Oxford [Oxfordshire] .
Written in English

    Subjects:
  • Class field theory.

  • Edition Notes

    StatementKenkichi Iwasawa.
    SeriesOxford mathematical monographs
    Classifications
    LC ClassificationsQA247 .I95413 1986
    The Physical Object
    Paginationviii, 155 p. ;
    Number of Pages155
    ID Numbers
    Open LibraryOL2546578M
    ISBN 100195040309
    LC Control Number85028462

    This book provides a readable introduction to local class field theory, a theory of algebraic extensions. It covers abelian extensions in particular of so-called local fields, typical examples of which are the p Format: Hardcover. This book provides a readable introduction to local class field theory, a theory of algebraic extensions. It covers abelian extensions in particular of so-called local fields, typical examples of which are the p .

    Introduction to Classical Field Theory Charles G. Torre Department of Physics, Utah State University, @ theory. This book re ects an alternative approach to learning classical eld quantum eld theory some day, this class should help out quite a bit. In mathematics, class field theory is the branch of algebraic number theory concerned with the abelian extensions of number fields, global fields of positive characteristic, and local theory had its origins in the proof of quadratic reciprocity by Gauss at the end of the 18th century. These ideas were developed over the next century, giving rise to a set of conjectures by Hilbert.

    A Gentle Course in Local Class Field Theory: Local Number Fields, Brauer Groups, Galois Cohomology | Pierre Guillot | download | B–OK. Download books for free. Find books. The goal of this book is to present local class field theory from the cohomo logical 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.


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Local class field theory by Kenkichi Iwasawa Download PDF EPUB FB2

The goal of this book is to present local class field theory from the cohomo­ logical 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. This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a Local class field theory book of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology.5/5(1).

This book provides a readable introduction to local class field theory, a theory of algebraic extensions. It covers abelian extensions in particular of so-called local fields, typical examples of which are the p-adic number fields.

The book is almost self-contained and is accessible to any reader with a basic background in algebra and topological groups. $\begingroup$ For local class field theory, look at Iwasawa's beautiful book "Local Class Field Theory". It is out of print, so find it in a library. It is out of print, so find it in a library.

You should have a vague understanding of the use of complex multiplication to generate abelian extensions of imaginary quadratic fields first, in order. The goal of this book is to present local class field theory from the cohomo- logical 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/5(7). Local class field theory is a theory of abelian extensions of so-called local fields, typical examples of which are the p-adic number fields.

This book is an introduction to that theory. Historically, local class field theory branched off from global, or classical. Basic Number Theory is an influential book by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic in part on a course taught at Princeton University init appeared as Volume in Springer's Grundlehren der mathematischen Wissenschaften series.

The approach handles all 'A-fields' or global fields. I Local Class Field Theory: Lubin-Tate Theory19 He wrote a very influential book on algebraic number theory inwhich gave the first systematic account of the theory.

Some of his famous problems were on number theory, and have also been influential. TAKAGI (–). He proved the fundamental theorems of abelian class field theory.

Class Field Theory. pdf file for the current version () Same file with margins cropped. This is a course on Class Field Theory, roughly along the lines of Artin and Tate and of the articles of Serre and Tate in Cassels-Fröhlich, except that the notes are more detailed and cover more.

This book provides a readable introduction to local class field theory, a theory of algebraic extensions. It covers abelian extensions in particular of so-called local fields, typical examples of which are the p-adic number fields.5/5(1).

The goal of this book is to present local class field theory from the cohomo logical 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. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields.

The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality : Springer International Publishing. This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group : Pierre Guillot.

the main results of local class field theory we review all other approaches to it in the new section 7. The new section 8 presents to the reader a recent noncommutative reciprocity map, which is not a homomorphism but a Galois 1-cycle.

This theory is based a generalization of the approach to (abelian) class field theory in this book. The goal of this book is to present local class field theory from the cohomo- logical 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.

This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology.

Namely, local class field theory is a subject which has been infinitely written about. Besides the various books on class field theory there are countless well-written, more conciseaccounts of class field theory (both local and global) available on the internet, covering the theory from essentially all angles.

The local Langlands Conjecture for GL(n) postulates the existence of a canonical bijection between such objects and n-dimensional representations of the Weil group, generalizing class field theory. This conjecture has now been proved for all F and n, but the arguments are.

s, establishing global class eld theory. Curiously, the global case was dealt before local class eld theory was in-troduced, despite the fact that modern treatments of global class eld theory use local class eld theory in constructing the Artin reciprocity map.

Local elds such as the p-adic rational numbers were de ned only in the late s by. This book provides a readable introduction to local class field theory, a theory of algebraic extensions, in particular abelian extensions of so-called local fields.

Rating: (not yet rated) 0 with reviews -. Local Class Field Theory. Serre, Jean-Pierre. Local Fields. Vol. New York, NY: Springer, ISBN: A classic reference that rewards the effort you put into it. It begins with the structure theory of local fields, develops group cohomology from scratch, and then proves the main theorem of local class field theory.This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory.

It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology. The book culminates with the description of the abelian extensions.I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely group­ theoretical principle, admitting an entirely elementary description.

This de­ scription makes possible a new foundation for the entire theory.