Multiplicities and Chern Classes in Local Algebra

Multiplicities and Chern Classes in Local Algebra

by Paul C. Roberts
     
 

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ISBN-10: 0521473160

ISBN-13: 9780521473163

Pub. Date: 12/28/2004

Publisher: Cambridge University Press

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

Overview

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.

Product Details

ISBN-13:
9780521473163
Publisher:
Cambridge University Press
Publication date:
12/28/2004
Series:
Tracts in Mathematics Series, #133
Pages:
317
Product dimensions:
5.98(w) x 8.98(h) x 0.87(d)

Table of Contents

1. Prime ideals and the Chow group; 2. Graded rings and Samuel multiplicity; 3. Complexes and derived functors; 4. Homological properties of rings and modules; 5. Intersection multiplicities; 6. The homological conjectures; 7. The Frobenius map; 8. Projective schemes; 9. Chern classes of locally free sheaves; 10. The Grassmannian; 11. Local Chern characters; 12. Properties of local Chern characters; 13. Applications and examples.

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