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.
Quadratic Forms, Linear Algebraic Groups, and Cohomology
Quadratic Forms, Linear Algebraic Groups, and 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 Quadratic Forms, Linear Algebraic Groups, and Cohomology write by Skip Garibaldi. This book was released on 2010-07-16. Quadratic Forms, Linear Algebraic Groups, and Cohomology available in PDF, EPUB and Kindle. 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.
Higher Segal Spaces
Higher Segal Spaces - 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 Higher Segal Spaces write by Tobias Dyckerhoff. This book was released on 2019-10-17. Higher Segal Spaces available in PDF, EPUB and Kindle. This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a simplicial space satisfying locality conditions related to triangulations of d-dimensional cyclic polytopes. Focus here is on the 2-dimensional case. Many important constructions are shown to exhibit the 2-Segal property, including Waldhausen’s S-construction, Hecke-Waldhausen constructions, and configuration spaces of flags. The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed. Higher Segal Spaces marks the beginning of a program to systematically study d-Segal spaces in all dimensions d. The elementary formulation of 2-Segal spaces in the opening chapters is accessible to readers with a basic background in homotopy theory. A chapter on Bousfield localizations provides a transition to the general theory, formulated in terms of combinatorial model categories, that features in the main part of the book. Numerous examples throughout assist readers entering this exciting field to move toward active research; established researchers in the area will appreciate this work as a reference.
Surveys on surgery theory : papers dedicated to C.T.C. Wall.
Surveys on surgery theory : papers dedicated to C.T.C. Wall. - 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 Surveys on surgery theory : papers dedicated to C.T.C. Wall. write by Sylvain Cappell. This book was released on 2000. Surveys on surgery theory : papers dedicated to C.T.C. Wall. 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).
