Sheaf Cohomology Course Notes, Spring 2010
نویسنده
چکیده
Overview 1 1. Mymotivation: K-theory of schemes 2 2. First steps in homological algebra 3 3. The long exact sequence 6 4. Derived functors 8 5. Cohomology of sheaves 10 6. Cohomology of a Noetherian Affine Scheme 12 7. Čech cohomology of sheaves 12 8. The Cohomology of Projective Space 14 9. Sheaf cohomology on P̃2 16 10. Pushing around sheaves, especially by the Frobenius 17 11. A first look at Frobenius splitting 19 12. Ext groups and sheaves 22 13. The Serre Duality Theorem 24 14. Higher Direct Images of Sheaves 28 15. Higher direct images: an example 30 16. Flat morphisms 31 17. Smooth morphisms 35 18. The Theorem on Formal Functions 36 19. Equivariant K-theory 37 References 38
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