Description
CAMBRIDGE Multiplicities and Chern Classes in Local Algebra 2004 Edition by Paul C. Roberts
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. 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.