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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