A finite-type morphism can have a proper fiber over every closed point without being proper. Properness controls compatible specialization in families, as expressed by the valuative criterion for properness, rather than only the individual closed fibers.

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  1. Proper 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
  10. Home

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