LECTURES ON THE K-FUNCTOR IN ALGEBRAIC GEOMETRY

Abstract

CONTENTS Introduction Guide to the literature § 1. The Grothendieck groups and § 2. and cycles § 3. Self-intersection and exterior powers § 4. Projectivized bundles § 5. Computation of and the splitting principle § 6. Computation of (conclusion) § 7. as a covariant functor § 8. -filtration of the ring § 9. Filtration and dimension § 10. The connection between and § 11. Chern classes and the Adams operation § 12. The structure of monoidal transformations § 13. The behaviour of under a monoidal transformation § 14. The behaviour of under a monoidal transformation (continuation) § 15. The behaviour of under a monoidal transformation (conclusion) § 16. The Adams operations and the homomorphism of the direct image § 17. The sheaf of differentials § 18. The Riemann-Roch theorem for embeddings § 19. The Riemann-Roch theorem for projections References