The Norm Residue Theorem In Motivic Cohomology
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The Norm Residue Theorem in Motivic Cohomology
Author | : Christian Haesemeyer,Charles A. Weibel |
Publsiher | : Princeton University Press |
Total Pages | : 316 |
Release | : 2019-06-11 |
Genre | : Mathematics |
ISBN | : 9780691191041 |
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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 The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky’s proof and introduce the key figures behind its development.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.
The Norm Residue Theorem in Motivic Cohomology
Author | : Christian Haesemeyer,Charles A. Weibel |
Publsiher | : Princeton University Press |
Total Pages | : 320 |
Release | : 2019-06-11 |
Genre | : Mathematics |
ISBN | : 9780691189635 |
Download The Norm Residue Theorem in Motivic Cohomology Book in PDF, Epub and Kindle
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 The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky’s proof and introduce the key figures behind its development.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.
Lecture Notes on Motivic Cohomology
Author | : Carlo Mazza,Vladimir Voevodsky,Charles A. Weibel |
Publsiher | : American Mathematical Soc. |
Total Pages | : 240 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821838474 |
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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).
The Bloch Kato Conjecture for the Riemann Zeta Function
Author | : John Coates,A. Raghuram,Anupam Saikia,R. Sujatha |
Publsiher | : Cambridge University Press |
Total Pages | : 317 |
Release | : 2015-03-13 |
Genre | : Mathematics |
ISBN | : 9781107492967 |
Download The Bloch Kato Conjecture for the Riemann Zeta Function Book in PDF, Epub and Kindle
A graduate-level account of an important recent result concerning the Riemann zeta function.
The K book
Author | : Charles A. Weibel |
Publsiher | : American Mathematical Soc. |
Total Pages | : 634 |
Release | : 2013-06-13 |
Genre | : Mathematics |
ISBN | : 9780821891322 |
Download The K book Book in PDF, Epub and Kindle
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
Quadratic Forms Linear Algebraic Groups and Cohomology
Author | : Skip Garibaldi,R. Sujatha,Venapally Suresh |
Publsiher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2010-07-16 |
Genre | : Mathematics |
ISBN | : 9781441962119 |
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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.
Advanced Modern Algebra
Author | : Joseph J. Rotman |
Publsiher | : American Mathematical Society |
Total Pages | : 570 |
Release | : 2023-02-22 |
Genre | : Mathematics |
ISBN | : 9781470472757 |
Download Advanced Modern Algebra Book in PDF, Epub and Kindle
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.
The Arithmetic and Geometry of Algebraic Cycles
Author | : B. Brent Gordon |
Publsiher | : American Mathematical Soc. |
Total Pages | : 468 |
Release | : 2000-01-01 |
Genre | : Mathematics |
ISBN | : 0821870203 |
Download The Arithmetic and Geometry of Algebraic Cycles Book in PDF, Epub and Kindle
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.