This exercise has H = 2; ex II.2.4 can be used; V = ....
For part a, let be a closed immersion and any morphism.
- Either argue locally and glue, or show the latter be a closed subset of
- Arguing locally would involve showing that if is locally and is locally , then the fiber product is locally .
- I'd say skip b) in favor of a much simpler proof using qcoh sheafs of ideals presented in section II.5.
- part c, the statement of topological spaces is clear, it remains to show the statement on the level of sheaves, reduce to the affine case:
- part d, to determine what should be just look locally.
- Let , then is an open set and the morphism here is determined by (ex. II.2.4). Take the kernel to construct a sheaf of ideals in X that will define Y.