Multiplicities and Chern Classes in Local Algebraby Paul C. Roberts
Pub. Date: 06/19/2008
Publisher: Cambridge University Press
In recent years there have been new developments in the field of commutative algebra which led to proofs of several conjectures which had been open for many years. Many of these proofs rely on techniques from topology and algebraic geometry, making them difficult for students and even researchers specializing in algebra to read. This book describes the mathematical background necessary to prove these results and sets them in their algebraic context.
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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