We will go over some properties of factorial schemes, then move on to chapter 6 on morphisms of shemes.
Read Section 6.1 giving motivation for morphisms. Read the definition 6.2.1 of morphism of ringed spaces. You have already seen the definition of isomorphism of ringed space, so the definition should be expected.
- Exercise 6.2.A. A morphism of ringed spaces can be given as a compatible family of morphisms on an open cover.
- 6.2.B. A morphisms of ringed spaces induces a functor on categories of O-modules.
- 6.2.C. A morphism induces a map on stalks.
- 6.2.D. A ring homomorphism induces a morphism of ringed spaces.
Read definition 6.3.1 on morphisms of locally ringed spaces and definition 6.3.3. on morphisms of schemes.
- Key exercise: 6.3.B.