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Author: Luis Ribes
Publisher: Springer Science & Business Media
Published: 2013-04-09
Total Pages: 441
ISBN-13: 3662040972
DOWNLOAD EBOOKThis 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.
Author: Luis Ribes
Publisher: Kingston, Ont., Queen's University
Published: 1970
Total Pages: 336
ISBN-13:
DOWNLOAD EBOOKAuthor: Grégory Berhuy
Publisher: Cambridge University Press
Published: 2010-09-09
Total Pages: 328
ISBN-13: 1139490885
DOWNLOAD EBOOKThis 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: David Harari
Publisher: Springer Nature
Published: 2020-06-24
Total Pages: 336
ISBN-13: 3030439011
DOWNLOAD EBOOKThis 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: Helmut Koch
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 196
ISBN-13: 3662049678
DOWNLOAD EBOOKHelmut 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: Luis Ribes
Publisher:
Published: 1970
Total Pages: 316
ISBN-13:
DOWNLOAD EBOOKAuthor: Moshe Jarden
Publisher: Springer Science & Business Media
Published: 2011-01-03
Total Pages: 313
ISBN-13: 3642151280
DOWNLOAD EBOOKAssuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields". Among others, it leads to the solution of two central results in "Field Arithmetic": (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$.
Author: Pierre Guillot
Publisher: Cambridge University Press
Published: 2018-11
Total Pages: 309
ISBN-13: 1108421776
DOWNLOAD EBOOKA self-contained exposition of local class field theory for students in advanced algebra.
Author: John S. Wilson
Publisher: Clarendon Press
Published: 1998-10-01
Total Pages: 302
ISBN-13: 0191589217
DOWNLOAD EBOOKThis is the first book to be dedicated entirely to profinite groups, an area of algebra with important links to number theory and other areas of mathematics. It provides a comprehensive overview of the subject; prerequisite knowledge is kept to a minimum, and several major theorems are presented in an accessible form. The book would provide a valuable introduction for postgraduate students, or form a useful reference for researchers in other areas. The first few chapters lay the foundations and explain the role of profinite groups in number theory. Later chapters explore various aspects of profinite groups in more detail; these contain accessible and lucid accounts of many major theorems. Prerequisites are kept to a minimum with the basic topological theory summarized in an introductory chapter.
Author: Charles A. Weibel
Publisher: Cambridge University Press
Published: 1995-10-27
Total Pages: 470
ISBN-13: 113964307X
DOWNLOAD EBOOKThe landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.
