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An Introduction To Galois Cohomology And Its Applications
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Book Synopsis An Introduction to Galois Cohomology and its Applications by : Grégory Berhuy
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.
Book Synopsis Central Simple Algebras and Galois Cohomology by : Philippe Gille
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.
Book Synopsis Galois Cohomology and Class Field Theory by : David Harari
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.
Book Synopsis Central Simple Algebras and Galois Cohomology by : Philippe Gille
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 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev–Suslin theorem, a 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, the text covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi–Brauer varieties, and techniques in Milnor K-theory and K-cohomology, leading to a full proof of the Merkurjev–Suslin theorem and its application to the characterization of reduced norms. The final chapter rounds off the theory by presenting the results in positive characteristic, including the theorems of Bloch–Gabber–Kato and Izhboldin. This second edition has been carefully revised and updated, and contains important additional topics.
Book Synopsis Galois Theory of p-Extensions by : Helmut Koch
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.
Book Synopsis Galois Theory and Cohomology of Commutative Rings by : Stephen Urban Chase
Download or read book Galois Theory and Cohomology of Commutative Rings written by Stephen Urban Chase and published by American Mathematical Soc.. This book was released on 1969 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Unramified Brauer Group and Its Applications by : Sergey Gorchinskiy
Download or read book Unramified Brauer Group and Its Applications written by Sergey Gorchinskiy and published by American Mathematical Soc.. This book was released on 2018-09-10 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to arithmetic geometry with special attention given to the unramified Brauer group of algebraic varieties and its most striking applications in birational and Diophantine geometry. The topics include Galois cohomology, Brauer groups, obstructions to stable rationality, Weil restriction of scalars, algebraic tori, the Hasse principle, Brauer-Manin obstruction, and étale cohomology. The book contains a detailed presentation of an example of a stably rational but not rational variety, which is presented as series of exercises with detailed hints. This approach is aimed to help the reader understand crucial ideas without being lost in technical details. The reader will end up with a good working knowledge of the Brauer group and its important geometric applications, including the construction of unirational but not stably rational algebraic varieties, a subject which has become fashionable again in connection with the recent breakthroughs by a number of mathematicians.
Book Synopsis Local Cohomology and Its Applications by : Gennady Lybeznik
Download or read book Local Cohomology and Its Applications written by Gennady Lybeznik and published by CRC Press. This book was released on 2001-10-18 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects presentations from the international workshop on local cohomology held in Guanajuato, Mexico, including expanded lecture notes of two minicourses on applications in equivariant topology and foundations of duality theory, and chapters on finiteness properties, D-modules, monomial ideals, combinatorial analysis, and related topics. Featuring selected papers from renowned experts around the world, Local Cohomology and Its Applications is a provocative reference for algebraists, topologists, and upper-level undergraduate and graduate students in these disciplines.
Book Synopsis Galois Cohomology by : Jean-Pierre Serre
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.
Book Synopsis Lecture Notes on Motivic Cohomology by : Carlo Mazza
Download or read book Lecture Notes on Motivic Cohomology written by Carlo Mazza and published by American Mathematical Soc.. This book was released on 2006 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of a motive is an elusive one, like its namesake "the motif" of Cezanne's impressionist method of painting. Its existence was first suggested by Grothendieck in 1964 as the underlying structure behind the myriad cohomology theories in Algebraic Geometry. We now know that there is a triangulated theory of motives, discovered by Vladimir Voevodsky, which suffices for the development of a satisfactory Motivic Cohomology theory. However, the existence of motives themselves remains conjectural. This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, etale cohomology, and Chow groups. The book is divided into lectures, grouped in six parts. The first part presents the definition of Motivic Cohomology, based upon the notion of presheaves with transfers. Some elementary comparison theorems are given in this part. The theory of (etale, Nisnevich, and Zariski) sheaves with transfers is developed in parts two, three, and six, respectively. The theoretical core of the book is the fourth part, presenting the triangulated category of motives. Finally, the comparison with higher Chow groups is developed in part five. The lecture notes format is designed for the book to be read by an advanced graduate student or an expert in a related field. The lectures roughly correspond to one-hour lectures given by Voevodsky during the course he gave at the Institute for Advanced Study in Princeton on this subject in 1999-2000. In addition, many of the original proofs have been simplified and improved so that this book will also be a useful tool for research mathematicians. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
Book Synopsis The Brauer–Grothendieck Group by : Jean-Louis Colliot-Thélène
Download or read book The Brauer–Grothendieck Group written by Jean-Louis Colliot-Thélène and published by Springer Nature. This book was released on 2021-07-30 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer–Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong’s proof of Gabber’s theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer–Manin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer–Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.
Book Synopsis The Maximal Subgroups of the Low-Dimensional Finite Classical Groups by : John N. Bray
Download or read book The Maximal Subgroups of the Low-Dimensional Finite Classical Groups written by John N. Bray and published by Cambridge University Press. This book was released on 2013-07-25 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classifies the maximal subgroups of the finite groups of Lie type up to dimension 12, using theoretical and computational methods.
Book Synopsis Topics in Galois Theory by : Jean-Pierre Serre
Download or read book Topics in Galois Theory written by Jean-Pierre Serre and published by CRC Press. This book was released on 2016-04-19 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt constructi
Book Synopsis Surveys in Combinatorics 2011 by : Robin Chapman
Download or read book Surveys in Combinatorics 2011 written by Robin Chapman and published by Cambridge University Press. This book was released on 2011-06-23 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles based on the invited lectures given at the 23rd British Combinatorial Conference, held in July 2011 at the University of Exeter. Each article surveys an area of current research in combinatorial mathematics and will be invaluable to anyone wishing to keep abreast of modern developments.
Book Synopsis Non-abelian Fundamental Groups and Iwasawa Theory by : John Coates
Download or read book Non-abelian Fundamental Groups and Iwasawa Theory written by John Coates and published by Cambridge University Press. This book was released on 2011-12-15 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the interaction between several key aspects of Galois theory based on Iwasawa theory, fundamental groups and automorphic forms. These ideas encompass a large portion of mainstream number theory and ramifications that are of interest to graduate students and researchers in number theory, algebraic geometry, topology and physics.
Book Synopsis Harmonic and Subharmonic Function Theory on the Hyperbolic Ball by : Manfred Stoll
Download or read book Harmonic and Subharmonic Function Theory on the Hyperbolic Ball written by Manfred Stoll and published by Cambridge University Press. This book was released on 2016-06-30 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive monograph is ideal for established researchers in the field and also graduate students who wish to learn more about the subject. The text is made accessible to a broad audience as it does not require any knowledge of Lie groups and only a limited knowledge of differential geometry. The author's primary emphasis is on potential theory on the hyperbolic ball, but many other relevant results for the hyperbolic upper half-space are included both in the text and in the end-of-chapter exercises. These exercises expand on the topics covered in the chapter and involve routine computations and inequalities not included in the text. The book also includes some open problems, which may be a source for potential research projects.
Book Synopsis Reversibility in Dynamics and Group Theory by : Anthony G. O'Farrell
Download or read book Reversibility in Dynamics and Group Theory written by Anthony G. O'Farrell and published by Cambridge University Press. This book was released on 2015-05-28 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible yet systematic account of reversibility that demonstrates its impact throughout many diverse areas of mathematics.
