On Some Properties of Motivic Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Some Properties of Motivic Cohomology write by Bertrand J. Guillou. This book was released on 2008. On Some Properties of Motivic Cohomology available in PDF, EPUB and Kindle.
Lecture Notes on Motivic Cohomology
Lecture Notes on Motivic Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lecture Notes on Motivic Cohomology write by Carlo Mazza. This book was released on 2006. Lecture Notes on Motivic Cohomology available in PDF, EPUB and Kindle. 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).
Cycles, Transfers, and Motivic Homology Theories. (AM-143)
Cycles, Transfers, and Motivic Homology Theories. (AM-143) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Cycles, Transfers, and Motivic Homology Theories. (AM-143) write by Vladimir Voevodsky. This book was released on 2000. Cycles, Transfers, and Motivic Homology Theories. (AM-143) available in PDF, EPUB and Kindle. The original goal that ultimately led to this volume was the construction of "motivic cohomology theory," whose existence was conjectured by A. Beilinson and S. Lichtenbaum. This is achieved in the book's fourth paper, using results of the other papers whose additional role is to contribute to our understanding of various properties of algebraic cycles. The material presented provides the foundations for the recent proof of the celebrated "Milnor Conjecture" by Vladimir Voevodsky. The theory of sheaves of relative cycles is developed in the first paper of this volume. The theory of presheaves with transfers and more specifically homotopy invariant presheaves with transfers is the main theme of the second paper. The Friedlander-Lawson moving lemma for families of algebraic cycles appears in the third paper in which a bivariant theory called bivariant cycle cohomology is constructed. The fifth and last paper in the volume gives a proof of the fact that bivariant cycle cohomology groups are canonically isomorphic (in appropriate cases) to Bloch's higher Chow groups, thereby providing a link between the authors' theory and Bloch's original approach to motivic (co-)homology.
Lecture Notes on Motivic Cohomology
Lecture Notes on Motivic Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lecture Notes on Motivic Cohomology write by Carlo Mazza. This book was released on 2006. Lecture Notes on Motivic Cohomology available in PDF, EPUB and Kindle. 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.
Motivic Homotopy Theory
Motivic Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Motivic Homotopy Theory write by Bjorn Ian Dundas. This book was released on 2007-07-11. Motivic Homotopy Theory available in PDF, EPUB and Kindle. 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.
