Algebraic Geometry - Schemes (1)

1. Sheaves on topological spaces
2. Affine schemes
3. Schemes and morphisms between them.
4. Quasi-coherent sheaves
5. Separated and proper morphisms.
6. Vector bundles and the Picard group of a scheme.
7. The functor of points and moduli spaces.
8. Morphisms to projective space and blow-ups.
9. Smooth morphisms and differential forms.
10. Sheaf cohomology.
11. Group schemes.

The course will be in English . It will continue in the Spring semester, as: Algebraic Geometry - Schemes (2)

Course Topics (tentative, for both semesters; more details in course web site):

1. Sheaves on topological spaces.
2. Ringed spaces.
3. Affine Schemes.
4. Schemes.
5. Maps of schemes.
6. Morphisms to projective space and blow-ups.
7. Calculating some invariants.
8. The functor of points and moduli spaces.
9. Algebraic differential calculus.
10. Group schemes and their Lie algebras.