Last edited by Kerisar
Monday, August 10, 2020 | History

9 edition of Class Field Theory found in the catalog.

Class Field Theory

From Theory to Practice

by Georges Gras

  • 361 Want to read
  • 2 Currently reading

Published by Springer .
Written in English

    Subjects:
  • Algebraic number theory,
  • Algebraic Fields,
  • Mathematics,
  • Science/Mathematics,
  • Number Theory,
  • Abelian closure,
  • Mathematics / Number Theory,
  • idele groups,
  • number fields,
  • reciprocity laws,
  • Group Theory,
  • Class field theory

  • Edition Notes

    ContributionsH. Cohen (Translator)
    The Physical Object
    FormatHardcover
    Number of Pages491
    ID Numbers
    Open LibraryOL9057909M
    ISBN 103540441336
    ISBN 109783540441335

    Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. ( views) Lectures on Field Theory and Ramification Theory by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay, These are notes of a series of lectures, aimed at covering the essentials of Field Theory and Ramification Theory as may be needed for local and global class field theory.

    Product Information. Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imper spicuous system of arguments which have tended to jump around all over the place. 3. The General Residue Class Field 90 4. General Local Class Field Theory 92 5. The Conductor 99 Appendix: Induced Characters Chapter XII. Explicit Reciprocity Laws 1. Formalism of the Power Residue Symbol 2. Local Analysis 3. Computation of the Norm Residue Symbol in Certain Local Kummer Fields 4. The Power Reciprocity Law.

    CFT Class Field Theory, v, He wrote a very influential book on algebraic number theory in , which 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, as. CHAPTER TWO CLASS FIELD THEORY §5. THE HILBERT CLASS FIELD AND p = x2 + ny2 In Chapter One, we used elementary techniques to study the primes - Selection from Primes of the Form x2+ny2: Fermat, Class Field Theory, and Complex Multiplication [Book].


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Class Field Theory by Georges Gras Download PDF EPUB FB2

Although I have learned cohomology of groups, I find that those theorems in the book are complicated and can not form a system. I'm wondering what are people's opinions of the book above, can you give me some suggestions on learning class field theory, and could.

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. The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory, and the authors accomplished this goal spectacularly: Class Field Theory book more than 40 years since its first publication, the book has served as an ultimate source for many generations of blackfin-boats.com by: This book is an accessible introduction to class field theory.

It takes a traditional approach in that it presents the global material first, using some of the original techniques of proof, but in a fashion that is cleaner and more streamlined than most other books on this topic.

Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical Author: Georges Gras.

Class Field Theory These pleasantly written notes, which cover the subject in detail, are a solid reference for most of the ideas of class field theory.

Texts by Neukirch. Neukirch, who was an exemplary expositor, wrote two books with the same name: Neukirch, Jürgen. Class Field Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, Buy Primes of the Form x2+ny2: Fermat, Class Field Theory, and Complex Multiplication, 2nd Edition on blackfin-boats.com FREE SHIPPING on qualified ordersCited by: Higher local class field theory is compatible with class field theory at the residue field level, using the border map of Milnor K-theory to create a commutative diagram involving the reciprocity map on the level of the field and the residue field.

General higher local class field theory was developed by Kazuya Kato and by Ivan Fesenko. Dec 17,  · The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory, and the authors accomplished this goal spectacularly: for more than 40 years since its first publication, the book has served.

Jürgen Neukirch: Class Field Theory-The Bonn Lectures Newly edited by Alexander Schmidt Author: Jürgen Neukirch (Alexander Schmidt, ed.) Title: Class Field Theory. The Bonn Lectures. Pages: Springer Textbook A pdf-file of the book, free for non-commercial use, can be downloaded here: 2.

Edition (May ). You have comments, found a. 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. Feb 19,  · So let’s posit a fairly well-prepared class. Say, graduate students who have taken their intro courses, so they have a fairly firm grasp of complex analysis, Galois Theory, and even a little topology.

And let’s say they have just finished their course in algebraic number theory, so studying class field theory is a natural next step.

Mar 15,  · This book explores the development of number theory, and class field theory in particular, as it passed through the hands of Emil Artin, Claude Chevalley, and Robert Langlands in the middle of the twentieth century.

The question of which primes can be written as the sum of two squares was settled by Euler. The more general question turns out to be much harder, and leads you to more advanced techniques in number theory like class field theory and elliptic curves with complex multiplication.

An exciting approach to the history and mathematics of number theory " the author's style is totally lucid and very easy to readthe result is - Selection from Primes of the Form x2+ny2: Fermat, Class Field Theory, and Complex Multiplication [Book].

Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study.

The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied. OCLC Number: Notes: "A chunk of the note of the Artin- Tate seminar on class field theory given at Princeton University innamely the part dealing with global class field theory (chapters 5 through 12) and the part dealing with the abstract theory of class formations and Weil groups (chapters ).".

Class field theory has a reputation of being an extremely beautiful part of number theory and an extremely difficult subject at the same time. For some-one with a good background in local fields, Galois cohomology and profinite groups there exist accounts of class field theory that reach the summit (exis.

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.

Finally, in order to bring class field theory down to earth, the book explores some of the magnificent formulas of complex multiplication. The central theme of the book is the story of which primes p can be expressed in the form x2 + ny2.

An incomplete answer is given using quadratic forms. A better though abstract answer comes from class field. Class Field Theory Abstract These notes are based on a course in class eld theory given by Freydoon Shahidi at Purdue University in the fall of The notes were typed by graduate students Daniel Shankman and Dongming She.

The approach to class eld theory in .That seems to be an advanced text with an algebraic take on class field theory.

I do not know that book personally, but after glancing through the PDF you linked, you'll probably need, at a minimum, a topology couse and a strong sequence of algebra courses.We remark that class field theory, and theory of cyclotomic fields, was once considered the key to Fermat's Last Theorem.

That approach was dramatically surpassed by the ideas of Frey, Serre, Ribet and Wiles. This paper demonstrates that class field theory still has a Author: Nuno Freitas, Alain Kraus, Samir Siksek.