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Multiplicities And Chern Classes In Local Algebra

Algebre Locale Multiplicites
Author: Paul C. Roberts
Publisher: Cambridge University Press
ISBN: 9780521473163
Size: 15.54 MB
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Presents the theory of local Chern characters used in commutative algebra in an algebraic setting.
Multiplicities and Chern Classes in Local Algebra
Language: en
Pages: 303
Authors: Paul C. Roberts, Paul Christopher Roberts
Categories: Mathematics
Type: BOOK - Published: 1998-05-13 - Publisher: Cambridge University Press
Presents the theory of local Chern characters used in commutative algebra in an algebraic setting.
Commutative Ring Theory
Language: en
Pages: 336
Authors: H. Matsumura
Categories: Mathematics
Type: BOOK - Published: 1989-05-25 - Publisher: Cambridge University Press
In addition to being an interesting and profound subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytical geometry. Matsumura covers the basic material, including dimension theory, depth, Cohen-Macaulay rings, Gorenstein rings, Krull rings and valuation rings. More advanced topics such as Ratliff's theorems on chains of prime ideals are also explored. The work is essentially self-contained, the only prerequisite being a sound knowledge of modern algebra, yet the reader is taken to the frontiers of the subject. Exercises are provided at the end of each section and solutions or hints to some of them are given at the end of the book.
Local Algebra
Language: en
Pages: 130
Authors: Jean-Pierre Serre
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media
This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.
Applications of Categorical Algebra
Language: en
Pages: 231
Authors: Alex Heller
Categories: Algebra, Homological
Type: BOOK - Published: 1970 - Publisher: American Mathematical Soc.
Books about Applications of Categorical Algebra
Cycles, Transfers, and Motivic Homology Theories. (AM-143), Volume 143
Language: en
Pages: 256
Authors: Vladimir Voevodsky, Andrei Suslin, Eric M. Friedlander
Categories: Mathematics
Type: BOOK - Published: 2011-11-12 - Publisher: Princeton University Press
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.
Cycles, Transfers, and Motivic Homology Theories. (AM-143)
Language: en
Pages: 254
Authors: Vladimir Voevodsky, Andrei Suslin, Eric M. Friedlander
Categories: Mathematics
Type: BOOK - Published: 2000 - Publisher: Princeton University Press
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.
Low Dimensional Topology
Language: en
Pages: 413
Authors: K. Böröczky, Walter David Neumann, András Stipsicz
Categories: Mathematics
Type: BOOK - Published: 1999 - Publisher: Bolyai Janos Matematikai Tarsulat
Books about Low Dimensional Topology
Algebraic Geometry for Beginners
Language: en
Pages: 354
Authors: C. Musili
Categories: Mathematics
Type: BOOK - Published: 2001-03-15 - Publisher: Springer
Books about Algebraic Geometry for Beginners
Algebraic Geometry
Language: en
Pages: 142
Authors: I. Dolgachev
Categories: Mathematics
Type: BOOK - Published: 2006-11-15 - Publisher: Springer
Books about Algebraic Geometry
Completion, Čech and Local Homology and Cohomology
Language: en
Pages: 346
Authors: Peter Schenzel, Anne-Marie Simon
Categories: Mathematics
Type: BOOK - Published: 2018-09-15 - Publisher: Springer
The aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas. A basic construction is the Čech complex with respect to a system of elements and its free resolution. The study of its homology and cohomology will play a crucial role in order to understand left derived functors of completion and right derived functors of torsion. This is useful for the extension and refinement of results known for modules to unbounded complexes in the more general setting of not necessarily Noetherian rings. The book is divided into three parts. The first one is devoted to modules, where the adic-completion functor is presented in full details with generalizations of some previous completeness criteria for modules. Part II is devoted to the study of complexes. Part III is mainly concerned with duality, starting with those between completion and torsion and leading to new aspects of various dualizing complexes. The Appendix covers various additional and complementary aspects of the previous investigations and also provides examples showing the necessity of the assumptions. The book is directed to readers