Multiplicities and Chern Classes in Local Algebra
Multiplicities and Chern Classes in Local Algebra
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.
- First book to give a thorough account of use of Chern classes in commutative algebra
- Does not require an extensive background in algebraic geometry
- Includes recent research results
Reviews & endorsements
"This book will be of enormous value to algebraists who want to gain an understanding of the powerful techniques presented in [F] and how they can be applied to local algebra." Bulletin of the AMS
"The book covers a variety of interesting subjects in commutative algebra and makes an algebraic version of the intersection theory accessible to a wide audience. It contains many new points of view, and the presentation is easy to follow. This is an excellent book." Mathematical Reviews
Product details
May 1998Hardback
9780521473163
320 pages
236 × 160 × 28 mm
0.636kg
Available
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.
