219,493pages on
this wiki
Add New Page
Discuss this page0 Share

This has H = 4 (can use II.3.11d, II.3.13, II.2.7), V = ....


  • First show f(Z) is separated and of finite type:
    • Recall cor. II.4.8, show the composition  Z \to X \to Y is proper.
    • Conclude the natural inclusion f(Z) \to Y is a closed immersion, hence of finite type and separated.
    • Conclude that f(Z) \to Y \to S is separated.
  • Properness:
    • For any Y' \to Y argue Y' \times Z \to Y' \times f(Z) is surjective. Can apply ex II.2.7
    • For any closed set C \subset Y' \times f(Z), have n(C) = (n \circ m)(m^{-1}(C)), where  Y' \times Z \xrightarrow{m} Y' \times f(Z) \xrightarrow{n} Y'

Ad blocker interference detected!

Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.

Also on Fandom

Random wikia