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Author : Klaus Haberland
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.3/5 (91 download)
Download or read book Galois Cohomology of Algebraic Number Fields written by Klaus Haberland and published by . This book was released on 1978 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jürgen Neukirch
Publisher : Springer Science & Business Media
ISBN 13 : 3540378898
Total Pages : 831 pages
Book Rating : 4.5/5 (43 download)
Download or read book Cohomology of Number Fields written by Jürgen Neukirch and published by Springer Science & Business Media. This book was released on 2013-09-26 with total page 831 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. In all it is a virtually complete treatment of a vast array of central topics in algebraic number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.
Author : Klaus Haberland
Publisher :
ISBN 13 :
Total Pages : 145 pages
Book Rating : 4.:/5 (174 download)
Download or read book Galois cohomology of algebraic number fields written by Klaus Haberland and published by . This book was released on 1978 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Harari
Publisher : Springer Nature
ISBN 13 : 3030439011
Total Pages : 336 pages
Book Rating : 4.0/5 (34 download)
Download or read book Galois Cohomology and Class Field Theory written by David Harari and published by Springer Nature. This book was released on 2020-06-24 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Grégory Berhuy
Publisher : Cambridge University Press
ISBN 13 : 1139490885
Total Pages : 328 pages
Book Rating : 4.1/5 (394 download)
Download or read book An Introduction to Galois Cohomology and its Applications written by Grégory Berhuy and published by Cambridge University Press. This book was released on 2010-09-09 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
ISBN 13 : 3642591418
Total Pages : 215 pages
Book Rating : 4.6/5 (425 download)
Download or read book Galois Cohomology written by Jean-Pierre Serre and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
ISBN 13 : 1475756739
Total Pages : 249 pages
Book Rating : 4.4/5 (757 download)
Download or read book Local Fields written by Jean-Pierre Serre and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.
Author : Pierre Guillot
Publisher : Cambridge University Press
ISBN 13 : 1108421776
Total Pages : 309 pages
Book Rating : 4.1/5 (84 download)
Download or read book A Gentle Course in Local Class Field Theory written by Pierre Guillot and published by Cambridge University Press. This book was released on 2018-11 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained exposition of local class field theory for students in advanced algebra.
Author : M. Ishida
Publisher : Springer
ISBN 13 : 3540375538
Total Pages : 123 pages
Book Rating : 4.5/5 (43 download)
Download or read book The Genus Fields of Algebraic Number Fields written by M. Ishida and published by Springer. This book was released on 2006-12-08 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: a
Author : Helmut Koch
Publisher : Springer Science & Business Media
ISBN 13 : 3662049678
Total Pages : 196 pages
Book Rating : 4.6/5 (62 download)
Download or read book Galois Theory of p-Extensions written by Helmut Koch and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : H. Koch
Publisher : Springer Science & Business Media
ISBN 13 : 3642580955
Total Pages : 274 pages
Book Rating : 4.6/5 (425 download)
Download or read book Algebraic Number Theory written by H. Koch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995
Author : Y. Ihara
Publisher : Springer Science & Business Media
ISBN 13 : 1461396492
Total Pages : 454 pages
Book Rating : 4.4/5 (613 download)
Download or read book Galois Groups over ? written by Y. Ihara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the offspring of a week-long workshop on "Galois groups over Q and related topics," which was held at the Mathematical Sciences Research Institute during the week March 23-27, 1987. The organizing committee consisted of Kenneth Ribet (chairman), Yasutaka Ihara, and Jean-Pierre Serre. The conference focused on three principal themes: 1. Extensions of Q with finite simple Galois groups. 2. Galois actions on fundamental groups, nilpotent extensions of Q arising from Fermat curves, and the interplay between Gauss sums and cyclotomic units. 3. Representations of Gal(Q/Q) with values in GL(2)j deformations and connections with modular forms. Here is a summary of the conference program: • G. Anderson: "Gauss sums, circular units and the simplex" • G. Anderson and Y. Ihara: "Galois actions on 11"1 ( ••• ) and higher circular units" • D. Blasius: "Maass forms and Galois representations" • P. Deligne: "Galois action on 1I"1(P-{0, 1, oo}) and Hodge analogue" • W. Feit: "Some Galois groups over number fields" • Y. Ihara: "Arithmetic aspect of Galois actions on 1I"1(P - {O, 1, oo})" - survey talk • U. Jannsen: "Galois cohomology of i-adic representations" • B. Matzat: - "Rationality criteria for Galois extensions" - "How to construct polynomials with Galois group Mll over Q" • B. Mazur: "Deforming GL(2) Galois representations" • K. Ribet: "Lowering the level of modular representations of Gal( Q/ Q)" • J-P. Serre: - Introductory Lecture - "Degree 2 modular representations of Gal(Q/Q)" • J.
Author : Philippe Gille
Publisher : Cambridge University Press
ISBN 13 : 1107156378
Total Pages : 431 pages
Book Rating : 4.1/5 (71 download)
Download or read book Central Simple Algebras and Galois Cohomology written by Philippe Gille and published by Cambridge University Press. This book was released on 2017-08-10 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive modern introduction to central simple algebra starting from the basics and reaching advanced results.
Author : J. S. Milne
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3/5 (97 download)
Download or read book Arithmetic Duality Theorems written by J. S. Milne and published by . This book was released on 1986 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
Author : Pierre Guillot
Publisher : Cambridge University Press
ISBN 13 : 1108386261
Total Pages : 309 pages
Book Rating : 4.1/5 (83 download)
Download or read book A Gentle Course in Local Class Field Theory written by Pierre Guillot and published by Cambridge University Press. This book was released on 2018-11-01 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of local number fields, as well as the celebrated Kronecker–Weber theory, in both the local and global cases. The material will find use across disciplines, including number theory, representation theory, algebraic geometry, and algebraic topology. Written for beginning graduate students and advanced undergraduates, this book can be used in the classroom or for independent study.
Author : Vladimir Platonov
Publisher : Academic Press
ISBN 13 : 0080874592
Total Pages : 629 pages
Book Rating : 4.0/5 (88 download)
Download or read book Algebraic Groups and Number Theory written by Vladimir Platonov and published by Academic Press. This book was released on 1993-12-07 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.
Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
ISBN 13 : 9780521004237
Total Pages : 164 pages
Book Rating : 4.0/5 (42 download)
Download or read book A Brief Guide to Algebraic Number Theory written by H. P. F. Swinnerton-Dyer and published by Cambridge University Press. This book was released on 2001-02-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
