Use the compatible pair and the notion of extension from (i). The valuative criterion for separatedness is
(1)
A quasi-separated morphism means one whose diagonal morphism is a quasi-compact morphism. A separated morphism automatically has this property because its diagonal morphism is a closed immersion. The quasi-separated morphism hypothesis is needed in the converse valuative test for arbitrary schemes. Existence is not demanded.[ref]

Ancestors (13)

  1. ii
  2. a
  3. 2
  4. 2023
  5. Past exam of the introduction to schemes course of the University of Oxford
  6. Introduction to schemes course of the University of Oxford
  7. Year 4 of the mathematics course of the University of Oxford
  8. Mathematics course of the University of Oxford
  9. Undergraduate course of the University of Oxford
  10. Course of the University of Oxford
  11. University of Oxford
  12. List of universities
  13. Home

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version