This meeting will continue with morphisms of schemes from Chapter 6.
Read carefully the proof of 6.3.2 (the key proposition: every morphism of locally ringed spaces between affine schemes is induced by a ring homomorphism). Someone will be asked to present the proof in class. We will break it into several steps. In particular,
- The map of points is determined by its map on global sections.
- The map of sections is determined by the map of global sections.
We will continue with various exercises:
- 6.3.D. The category of rings and the opposite category of affine schemes are equivalent.
- 6.3.C. A morphism of schemes is a morphism of ringed spaces that is locally a morphism of affine schemes.
Read section 6.3.4 and the definition of S-schemes. We have already seen a different definition of A-schemes. Show that this new definition is compatible with the old (exercise 6.3.G).
- 6.3.E. Practice with morphisms.
- 6.3.F. Morphisms X -> Spec A.