Lecture Notes On Motivic Cohomology

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Lecture Notes On Motivic Cohomology

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Author : Carlo Mazza
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Lecture Notes On Motivic Cohomology written by Carlo Mazza and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Homology theory categories.

Provides an account of the triangulated theory of motives. The book's 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, étale cohomology, and Chow groups.

Lecture Notes On Motivic Cohomology

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date :

Lecture Notes On Motivic Cohomology written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Motivic Homotopy Theory

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Author : Bjorn Ian Dundas
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-11

Motivic Homotopy Theory written by Bjorn Ian Dundas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-11 with Mathematics categories.

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.

The Norm Residue Theorem In Motivic Cohomology

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Author : Christian Haesemeyer
language : en
Publisher: Princeton University Press
Release Date : 2019-06-11

The Norm Residue Theorem In Motivic Cohomology written by Christian Haesemeyer and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Mathematics categories.

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.

Motives

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Author : Uwe Jannsen
language : en
Publisher:
Release Date : 1994

Motives written by Uwe Jannsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This volume contains the revised texts of the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle of 1991. A number of related works are also included, making for a total of forty-seven papers, from general introductions to specialized surveys to research papers.

The K Book

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Author : Charles A. Weibel
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-13

The K Book written by Charles A. Weibel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-13 with Mathematics categories.

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

The Arithmetic And Geometry Of Algebraic Cycles

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Author : B. Brent Gordon
language : en
Publisher: American Mathematical Soc.
Release Date : 2000-01-01

The Arithmetic And Geometry Of Algebraic Cycles written by B. Brent Gordon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.

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.

Motivic Integration And Its Interactions With Model Theory And Non Archimedean Geometry Volume 2

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Author : Raf Cluckers
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-22

Motivic Integration And Its Interactions With Model Theory And Non Archimedean Geometry Volume 2 written by Raf Cluckers and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-22 with Mathematics categories.

The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.

Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures

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Author : Bhatia Rajendra
language : en
Publisher: World Scientific
Release Date : 2011-06-06

Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures written by Bhatia Rajendra and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-06 with Mathematics categories.

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.

Motivic Aspects Of Hodge Theory

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Author : Chris Peters
language : en
Publisher:
Release Date : 2010

Motivic Aspects Of Hodge Theory written by Chris Peters and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Geometry, Algebraic categories.

These notes are based on a series of lectures given at the Tata Institute of Fundamental Research, Mumbai, in 2007, on the theme of Hodge theoretic motives associated to various geometric objects. Starting with the topological setting, the notes go on to Hodge theory and mixed Hodge theory on the cohomology of varieties. Degenerations, limiting mixed Hodge structures and the relation to singularities are addressed next. The original proof of Bittner's theorem on the Grothendieck group of varieties, with some applications, is presented as an appendix to one of the chapters. The situation of relative varieties is addressed next using the machinery of mixed Hodge modules. Chern classes for singular varieties are explained in the motivic setting using Bittner's approach, and their full functorial meaning is made apparent using mixed Hodge modules. An appendix explains the treatment of Hodge characteristic in relation with motivic integration and string theory. Throughout these notes, emphasis is placed on explaining concepts and giving examples.