Profinite Groups
Profinite Groups

Author: Luis Ribes

Publisher: Springer Science & Business Media

Published: 2013-04-09

Total Pages: 441

ISBN-13: 3662040972

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This self-contained book serves both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. It contains complete and clear proofs for most results, many of which appear here in book form for the first time. Suitable as a basis for courses.

An Introduction to Galois Cohomology and its Applications
An Introduction to Galois Cohomology and its Applications

Author: Grégory Berhuy

Publisher: Cambridge University Press

Published: 2010-09-09

Total Pages: 328

ISBN-13: 1139490885

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This is the first detailed elementary introduction to Galois cohomology and its applications. The introductory section is self-contained and provides the basic results of the theory. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.

Galois Cohomology and Class Field Theory
Galois Cohomology and Class Field Theory

Author: David Harari

Publisher: Springer Nature

Published: 2020-06-24

Total Pages: 336

ISBN-13: 3030439011

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This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. 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 theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.

Profinite Groups, Arithmetic, and Geometry. (AM-67), Volume 67
Profinite Groups, Arithmetic, and Geometry. (AM-67), Volume 67

Author: Stephen S. Shatz

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 264

ISBN-13: 1400881854

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In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective is to present effectively that body of material upon which all modern research in Diophantine geometry and higher arithmetic is based, and to do so in a manner that emphasizes the many interesting lines of inquiry leading from these foundations.

Galois Cohomology
Galois Cohomology

Author: Jean-Pierre Serre

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 215

ISBN-13: 3642591418

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This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.

Galois Theory of p-Extensions
Galois Theory of p-Extensions

Author: Helmut Koch

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 196

ISBN-13: 3662049678

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Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer, along with many additional recent references.