Multiplicities and Chern Classes in Local Algebra (Cambridge Tracts in Mathematics, Series Number 133)

The theory of local Chern characters used in commutative algebra originated in topology about thirty years ago, and from there was introduced in algebraic geometry. This book describes the theory in an algebraic setting, presenting recent research results and important algebraic applications, some of which come from the author's own work. It concentrates on the background in commutative algebra and homological algebra and describes the relations between these subjects, including extensive discussions of the homological conjectures and of the use of the Frobenius map. It will be particularly useful for graduate students and researchers. The Theory Of Local Chern Characters Used In Commutative Algebra Originated In Topology Some Years Ago, And From There Was Introduced In Algebraic Geometry. This Book Describes The Theory In An Algebraic Setting, Presenting Research Results And Important Algebraic Applications, Some Of Which Come From The Author's Own Work. It Concentrates On The Background In Commutative Algebra And Homological Algebra And Describes The Relations Between These Subjects, Including Extensive Discussions Of The Homological Conjectures And Of The Use Of The Frobenius Map. Prime Ideals And The Chow Group -- Graded Rings And Samuel Multiplicity -- Complexes And Derived Functors -- Homological Properties Of Rings And Modules -- Intersection Multiplicities -- The Homological Conjectures -- The Frobenius Map -- Projective Schemes -- Chern Classes Of Locally Free Sheaves -- The Grassmannian -- Local Chern Characters -- Properties Of Local Chern Characters -- Applications And Examples. Paul C. Roberts. Includes Bibliographical References (p. 297-300) And Index. This book gives a detailed account of recent work on relations between commutative algebra and intersection theory, with a particular emphasis on applications of the theory of local Chern characters. This theory is the result of many years of development, having originated in topology and been introduced in algebraic geometry about thirty years ago. Building on the algebraic form described in Intersection Theory by W. Fulton, Paul Roberts presents further developments and important algebraic applications that were not known at the time Fulton's book was written. Students and researchers specializing in commutative algebra will find access to a wide range of new ideas in this book

presents The Theory Of Local Chern Characters Used In Commutative Algebra In An Algebraic Setting.