Multiplicities and Chern Classes in Local Algebra

Presents the theory of local Chern characters used in commutative algebra in an algebraic setting.

Paul C. Roberts (Author)

9780521473163, Cambridge University Press

Hardback, published 13 May 1998

320 pages
23.6 x 16 x 2.8 cm, 0.636 kg

Review of the hardback: '… a well-motivated survey of such a broad range of material, some of it quite technical, which leads the reader to the forefront of some of the deepest modern developments in Intersection Theory.' Proceedings of the Edinburgh Mathematical Society

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.

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.

Subject Areas: Algebra [PBF]