| Bemerkung |
In the first semester of algebraic geometry, we outlined the foundations of the modern theory, the theory of schemes, giving basic definitions and constructions. We showed how the category of schemes enlarges the (opposite) category of commutative rings, gave tools for the construction of schemes by gluing, and showed the existence of arbitrary fiber products. We also discussed ``global'' properties of morphisms: finite, finite type, separable and proper morphisms, open and closed immersions, projective morphisms, and the construction of projective morphisms using the functor Proj. The second semester will deal with local properties of morphisms and with cohomology of coherent sheaves. |
