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.
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.
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.
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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