Multiplicities and Chern Classes in Local Algebra

ISBN-13: 9780521473163 / Angielski / Twarda / 1998 / 320 str.

Paul Roberts; B. Bollobas; W. Fulton

Opis

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.

Recenzje

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

Spis treści

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.