The Norm Residue Theorem In Motivic Cohomology

Author : Christian Haesemeyer,Charles A. Weibel
Publisher : Princeton University Press
Page : 316 pages
File Size : 53,8 Mb
Release : 2019-06-11
Category : Mathematics
ISBN : 9780691191041

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The Norm Residue Theorem in Motivic Cohomology by Christian Haesemeyer,Charles A. Weibel Pdf

This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky’s proof and introduce the key figures behind its development. They proceed to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. The book then addresses symmetric powers of motives and motivic cohomology operations. Comprehensive and self-contained, The Norm Residue Theorem in Motivic Cohomology unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.

Author : Christian Haesemeyer,Charles A. Weibel
Publisher : Princeton University Press
Page : 320 pages
File Size : 54,9 Mb
Release : 2019-06-11
Category : Mathematics
ISBN : 9780691189635

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The Norm Residue Theorem in Motivic Cohomology by Christian Haesemeyer,Charles A. Weibel Pdf

This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky’s proof and introduce the key figures behind its development. They proceed to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. The book then addresses symmetric powers of motives and motivic cohomology operations. Comprehensive and self-contained, The Norm Residue Theorem in Motivic Cohomology unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.

Author : Carlo Mazza,Vladimir Voevodsky,Charles A. Weibel
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 55,9 Mb
Release : 2006
Category : Mathematics
ISBN : 0821838474

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Lecture Notes on Motivic Cohomology by Carlo Mazza,Vladimir Voevodsky,Charles A. Weibel Pdf

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).

Author : John Coates,A. Raghuram,Anupam Saikia,R. Sujatha
Publisher : Cambridge University Press
Page : 317 pages
File Size : 48,8 Mb
Release : 2015-03-13
Category : Mathematics
ISBN : 9781107492967

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The Bloch-Kato Conjecture for the Riemann Zeta Function by John Coates,A. Raghuram,Anupam Saikia,R. Sujatha Pdf

A graduate-level account of an important recent result concerning the Riemann zeta function.

Author : Charles A. Weibel
Publisher : American Mathematical Soc.
Page : 634 pages
File Size : 48,7 Mb
Release : 2013-06-13
Category : Mathematics
ISBN : 9780821891322

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The $K$-book by Charles A. Weibel Pdf

Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr

Author : Skip Garibaldi,R. Sujatha,Venapally Suresh
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 55,5 Mb
Release : 2010-07-16
Category : Mathematics
ISBN : 9781441962119

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Quadratic Forms, Linear Algebraic Groups, and Cohomology by Skip Garibaldi,R. Sujatha,Venapally Suresh Pdf

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.

Author : Joseph J. Rotman
Publisher : American Mathematical Society
Page : 570 pages
File Size : 48,5 Mb
Release : 2023-02-22
Category : Mathematics
ISBN : 9781470472757

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Advanced Modern Algebra by Joseph J. Rotman Pdf

This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

Author : B. Brent Gordon
Publisher : American Mathematical Soc.
Page : 468 pages
File Size : 48,7 Mb
Release : 2000-01-01
Category : Mathematics
ISBN : 0821870203

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The Arithmetic and Geometry of Algebraic Cycles by B. Brent Gordon Pdf

From the June 1998 Summer School come 20 contributions that explore algebraic cycles (a subfield of algebraic geometry) from a variety of perspectives. The papers have been organized into sections on cohomological methods, Chow groups and motives, and arithmetic methods. Some specific topics include logarithmic Hodge structures and classifying spaces; Bloch's conjecture and the K-theory of projective surfaces; and torsion zero-cycles and the Abel-Jacobi map over the real numbers.

Author : Igor Kriz,Sophie Kriz
Publisher : Springer Nature
Page : 481 pages
File Size : 49,5 Mb
Release : 2021-03-13
Category : Mathematics
ISBN : 9783030626440

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Introduction to Algebraic Geometry by Igor Kriz,Sophie Kriz Pdf

The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained. The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.

Author : Guillermo Cortiñas
Publisher : European Mathematical Society
Page : 460 pages
File Size : 50,5 Mb
Release : 2008
Category : K-theory
ISBN : 3037190604

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K-theory and Noncommutative Geometry by Guillermo Cortiñas Pdf

Since its inception 50 years ago, K-theory has been a tool for understanding a wide-ranging family of mathematical structures and their invariants: topological spaces, rings, algebraic varieties and operator algebras are the dominant examples. The invariants range from characteristic classes in cohomology, determinants of matrices, Chow groups of varieties, as well as traces and indices of elliptic operators. Thus K-theory is notable for its connections with other branches of mathematics. Noncommutative geometry develops tools which allow one to think of noncommutative algebras in the same footing as commutative ones: as algebras of functions on (noncommutative) spaces. The algebras in question come from problems in various areas of mathematics and mathematical physics; typical examples include algebras of pseudodifferential operators, group algebras, and other algebras arising from quantum field theory. To study noncommutative geometric problems one considers invariants of the relevant noncommutative algebras. These invariants include algebraic and topological K-theory, and also cyclic homology, discovered independently by Alain Connes and Boris Tsygan, which can be regarded both as a noncommutative version of de Rham cohomology and as an additive version of K-theory. There are primary and secondary Chern characters which pass from K-theory to cyclic homology. These characters are relevant both to noncommutative and commutative problems and have applications ranging from index theorems to the detection of singularities of commutative algebraic varieties. The contributions to this volume represent this range of connections between K-theory, noncommmutative geometry, and other branches of mathematics.

Author : Anonim
Publisher : World Scientific
Page : 1191 pages
File Size : 40,6 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 8210379456XXX

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by Anonim Pdf

Author : Bhatia Rajendra,Pal Arup,Rangarajan G
Publisher : World Scientific
Page : 4144 pages
File Size : 51,6 Mb
Release : 2011-06-06
Category : Mathematics
ISBN : 9789814462938

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Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures by Bhatia Rajendra,Pal Arup,Rangarajan G Pdf

ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Author : Sinnou David
Publisher : Cambridge University Press
Page : 227 pages
File Size : 54,5 Mb
Release : 1996-11-07
Category : Mathematics
ISBN : 9780521585491

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Number Theory by Sinnou David Pdf

This book covers the whole spectrum of number theory, and is composed of contributions from some of the best specialists worldwide.

Author : B. Brent Gordon,James D. Lewis,Stefan Müller-Stach,Shuji Saito,Noriko Yui
Publisher : Springer Science & Business Media
Page : 652 pages
File Size : 51,5 Mb
Release : 2000-02-29
Category : Mathematics
ISBN : 0792361946

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The Arithmetic and Geometry of Algebraic Cycles by B. Brent Gordon,James D. Lewis,Stefan Müller-Stach,Shuji Saito,Noriko Yui Pdf

The subject of algebraic cycles has thrived through its interaction with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to such developments as a description of Chow groups in terms of algebraic K-theory, the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge and Tate, and the conjectures of Bloch and Beilinson. The immense recent progress in algebraic cycles, based on so many interactions with so many other areas of mathematics, has contributed to a considerable degree of inaccessibility, especially for graduate students. Even specialists in one approach to algebraic cycles may not understand other approaches well. This book offers students and specialists alike a broad perspective of algebraic cycles, presented from several viewpoints, including arithmetic, transcendental, topological, motives and K-theory methods. Topics include a discussion of the arithmetic Abel-Jacobi mapping, higher Abel-Jacobi regulator maps, polylogarithms and L-series, candidate Bloch-Beilinson filtrations, applications of Chern-Simons invariants to algebraic cycles via the study of algebraic vector bundles with algebraic connection, motivic cohomology, Chow groups of singular varieties, and recent progress on the Hodge and Tate conjectures for Abelian varieties.

Author : Eric Friedlander,Daniel R. Grayson
Publisher : Springer Science & Business Media
Page : 1148 pages
File Size : 54,9 Mb
Release : 2005-07-18
Category : Mathematics
ISBN : 9783540230199

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Handbook of K-Theory by Eric Friedlander,Daniel R. Grayson Pdf

This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.