Multiplicities and Chern Classes in Local Algebra

TRAMA

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.

NOTE EDITORE

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.

SOMMARIO

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.

PREFAZIONE

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. This book describes the mathematical background necessary to prove these results and sets them in their algebraic context.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780521473163
• Collana: Cambridge Tracts in Mathematics
• Dimensioni: 236 x 28 x 160 mm Ø 636 gr
• Formato: Copertina rigida
• Pagine Arabe: 320