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Author : Klaus Haberland,Helmut Koch,Thomas Zink
Publisher : Unknown
Page : 152 pages
File Size : 51,9 Mb
Release : 1978
Category : Algebraic fields
ISBN : UOM:39015015612628
Author : Klaus Haberland
Publisher : Unknown
Page : 145 pages
File Size : 42,6 Mb
Release : 1978
Category : Electronic
ISBN : OCLC:174354840
Author : Jürgen Neukirch,Alexander Schmidt,Kay Wingberg
Publisher : Springer Science & Business Media
Page : 831 pages
File Size : 44,9 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9783540378891
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 : Albrecht Fröhlich,London Mathematical Society
Publisher : Unknown
Page : 724 pages
File Size : 46,8 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:39015039010486
Author : David Harari
Publisher : Springer Nature
Page : 336 pages
File Size : 42,6 Mb
Release : 2020-06-24
Category : Mathematics
ISBN : 9783030439019
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 : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 45,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642591419
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 : Pierre Guillot
Publisher : Cambridge University Press
Page : 309 pages
File Size : 53,5 Mb
Release : 2018-11
Category : Mathematics
ISBN : 9781108421775
A self-contained exposition of local class field theory for students in advanced algebra.
Author : Philippe Gille,Tamás Szamuely
Publisher : Cambridge University Press
Page : 26 pages
File Size : 51,7 Mb
Release : 2006-08-10
Category : Mathematics
ISBN : 9781139458726
This book is the first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields. Starting from the basics, it reaches such advanced results as the Merkurjev-Suslin theorem. This theorem is both the culmination of work initiated by Brauer, Noether, Hasse and Albert and the starting point of current research in motivic cohomology theory by Voevodsky, Suslin, Rost and others. Assuming only a solid background in algebra, but no homological algebra, the book covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi-Brauer varieties, residue maps and, finally, Milnor K-theory and K-cohomology. The last chapter rounds off the theory by presenting the results in positive characteristic, including the theorem of Bloch-Gabber-Kato. The book is suitable as a textbook for graduate students and as a reference for researchers working in algebra, algebraic geometry or K-theory.
Author : Mikhail Borovoi
Publisher : American Mathematical Soc.
Page : 50 pages
File Size : 43,5 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821806500
In this volume, a new functor $H^2_{ab}(K,G)$ of abelian Galois cohomology is introduced from the category of connected reductive groups $G$ over a field $K$ of characteristic $0$ to the category of abelian groups. The abelian Galois cohomology and the abelianization map$ab^1:H^1(K,G) \rightarrow H^2_{ab}(K,G)$ are used to give a functorial, almost explicit description of the usual Galois cohomology set $H^1(K,G)$ when $K$ is a number field.
Author : Brian David Conrad
Publisher : American Mathematical Soc.
Page : 588 pages
File Size : 44,8 Mb
Release : 2024-07-03
Category : Mathematics
ISBN : 0821886916
The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.
Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 249 pages
File Size : 45,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475756739
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 : J. S. Milne
Publisher : Unknown
Page : 440 pages
File Size : 54,7 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39076000806617
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 : H. Koch
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580956
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 : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 40,9 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author : Skip Garibaldi,R. Sujatha,Venapally Suresh
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 53,9 Mb
Release : 2010-07-16
Category : Mathematics
ISBN : 9781441962119
Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.