The Norm Residue Theorem In Motivic Cohomology
Download The Norm Residue Theorem In Motivic Cohomology full books in PDF, epub, and Kindle. Read online free The Norm Residue Theorem In Motivic Cohomology ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: Christian Haesemeyer |
Publisher |
: Princeton University Press |
Total Pages |
: 316 |
Release |
: 2019-06-11 |
ISBN-10 |
: 9780691191041 |
ISBN-13 |
: 0691191042 |
Rating |
: 4/5 (41 Downloads) |
Synopsis The Norm Residue Theorem in Motivic Cohomology by : Christian Haesemeyer
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 The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky’s proof and introduce the key figures behind its development.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 |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 240 |
Release |
: 2006 |
ISBN-10 |
: 0821838474 |
ISBN-13 |
: 9780821838471 |
Rating |
: 4/5 (74 Downloads) |
Synopsis Lecture Notes on Motivic Cohomology by : Carlo Mazza
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 |
Publisher |
: Cambridge University Press |
Total Pages |
: 317 |
Release |
: 2015-03-19 |
ISBN-10 |
: 9781316241301 |
ISBN-13 |
: 1316241300 |
Rating |
: 4/5 (01 Downloads) |
Synopsis The Bloch–Kato Conjecture for the Riemann Zeta Function by : John Coates
There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings.
Author |
: B. Brent Gordon |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 652 |
Release |
: 2000-02-29 |
ISBN-10 |
: 0792361946 |
ISBN-13 |
: 9780792361947 |
Rating |
: 4/5 (46 Downloads) |
Synopsis The Arithmetic and Geometry of Algebraic Cycles by : B. Brent Gordon
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 |
: Charles A. Weibel |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 634 |
Release |
: 2013-06-13 |
ISBN-10 |
: 9780821891322 |
ISBN-13 |
: 0821891324 |
Rating |
: 4/5 (22 Downloads) |
Synopsis The $K$-book by : Charles A. Weibel
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 |
: Bjorn Ian Dundas |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 228 |
Release |
: 2007-07-11 |
ISBN-10 |
: 9783540458975 |
ISBN-13 |
: 3540458972 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Motivic Homotopy Theory by : Bjorn Ian Dundas
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
Author |
: Skip Garibaldi |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 344 |
Release |
: 2010-07-16 |
ISBN-10 |
: 9781441962119 |
ISBN-13 |
: 1441962115 |
Rating |
: 4/5 (19 Downloads) |
Synopsis Quadratic Forms, Linear Algebraic Groups, and Cohomology by : Skip Garibaldi
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 |
Total Pages |
: 570 |
Release |
: 2023-02-22 |
ISBN-10 |
: 9781470472757 |
ISBN-13 |
: 1470472759 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Advanced Modern Algebra by : Joseph J. Rotman
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 |
: Svetlin G. Georgiev |
Publisher |
: Walter de Gruyter GmbH & Co KG |
Total Pages |
: 404 |
Release |
: 2019-06-17 |
ISBN-10 |
: 9783110657722 |
ISBN-13 |
: 3110657724 |
Rating |
: 4/5 (22 Downloads) |
Synopsis Functional Analysis with Applications by : Svetlin G. Georgiev
This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study.
Author |
: Charles A. Weibel |
Publisher |
: Cambridge University Press |
Total Pages |
: 470 |
Release |
: 1995-10-27 |
ISBN-10 |
: 9781139643078 |
ISBN-13 |
: 113964307X |
Rating |
: 4/5 (78 Downloads) |
Synopsis An Introduction to Homological Algebra by : Charles A. Weibel
The 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.