Download or read book Cohomology of Arithmetic Groups and Automorphic Forms written by Jean-Pierre Labesse and published by Springer. This book was released on 2006-11-14 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp. the geometry of locally symmetric spaces. These proceedings will serve as a guide to this still rapidly developing area of mathematics. Besides two survey articles, the contributions are original research papers.
Download or read book Cohomology of Arithmetic Groups written by James W. Cogdell and published by Springer. This book was released on 2018-08-18 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the mathematical interests of Joachim Schwermer, who throughout his career has focused on the cohomology of arithmetic groups, automorphic forms and the geometry of arithmetic manifolds. To mark his 66th birthday, the editors brought together mathematical experts to offer an overview of the current state of research in these and related areas. The result is this book, with contributions ranging from topology to arithmetic. It probes the relation between cohomology of arithmetic groups and automorphic forms and their L-functions, and spans the range from classical Bianchi groups to the theory of Shimura varieties. It is a valuable reference for both experts in the fields and for graduate students and postdocs wanting to discover where the current frontiers lie.
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.
Download or read book Profinite Groups Arithmetic and Geometry written by Stephen S. Shatz and published by Princeton University Press. This book was released on 2016-03-02 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Manifolds and Lie Groups written by J. Hano and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the collection of papers dedicated to Yozo Matsushima on his 60th birthday, which took place on February 11, 1980. A conference in Geometry in honor of Professor Matsushima was held at the University of Notre Dame on May 14 and 15, 1980. Some of the papers in this volume were delivered on this occasion. 0 00 0\ - 15 S. Kobayashi, University 27 R. Ogawa, Loyola 42 P. Ryan, Indiana 1 W. Stoll 2 W. Kaup, University of of California at Berkeley University (Chicago) University at South Bend Tubing en 16 B.Y. Chen, 28 A. Howard 43 M. Kuga, SUNY at 3 G. Shimura, Michigan State University 29 D. Blair, Stony Brook Princeton University 17 G. Ludden, Michigan State University 44 W. Higgins 30 B. Smyth 4 A. Borel, Institute for Michigan State University 45 J. Curry Advanced Study 18 S. Harris, 31 A. Pradhan 46 D. Norris 32 R. Escobales, 5 Y. Matsushima University of Missouri 47 J. Spellecy Canisius College 6 Mrs. Matsushima 19 J. Beem, 48 M. Clancy 7 K. Nomizu, University of Missouri 33 L. Smiley 49 J. Rabinowitz, University 20 D. Collins, 34 C.H. Sung Brown University of Illinois at Chicago Valparaiso University 35 M. Markowitz 8 J.-1. Hano, 50 R. Richardson, Australian Washington University 36 A. Sommese 21 I. Satake, University of National University California at Berkeley 37 A. Vitter, 9 J. Carrell, University of 51 D. Lieberman, 22 H.
Download or read book Continuous Cohomology Discrete Subgroups and Representations of Reductive Groups written by Armand Borel and published by American Mathematical Soc.. This book was released on 2013-11-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.
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.
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.
Download or read book Arithmetic Groups and Their Generalizations written by Lizhen Ji and published by American Mathematical Soc.. This book was released on 2008 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.
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.
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.
Download or read book Cohomology of Groups written by Kenneth S. Brown and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.
Download or read book Eisenstein Cohomology for GLN and the Special Values of Rankin Selberg L Functions written by Günter Harder and published by Princeton University Press. This book was released on 2020 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- The cohomology of GLn -- Analytic tools -- Boundary cohomology -- The strongly inner spectrum and applications -- Eisenstein cohomology -- L-functions -- Harish-Chandra modules over Z / by Günter Harder -- Archimedean intertwining operator / by Uwe Weselmann.
Download or read book Etale Cohomology Theory written by Lei Fu and published by World Scientific. This book was released on 2011-01-31 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Edition available hereEtale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.
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.
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).
Download or read book Cohomology of Arithmetic Groups and Automorphic Forms written by Jean-Pierre Labesse and published by . This book was released on 2014-09-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
