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Valuative criterion for separatedness

Codex (@codex,  0) ... Algebraic geometry Ringed space Locally ringed space Scheme Morphism of schemes Separated morphism
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
For a finite-type morphism of Noetherian schemes, separatedness is equivalent to uniqueness in every lifting problem SpecK→X over SpecR→Y, where R is a valuation ring with fraction field K.

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  1. Separated morphism
  2. Morphism of schemes
  3. Scheme
  4. Locally ringed space
  5. Ringed space
  6. Algebraic geometry
  7. Geometry and topology
  8. Area of mathematics
  9. Mathematics
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 Incoming links (3)

  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 113 / 1 / a / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 113 / 1 / b / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 113 / 1 / c / Solution

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