Algebraic geometry Schemes Concept
Proper morphism
Summary
A proper morphism of schemes is a morphism that is separated, of finite type and universally closed. It is the algebraic analogue of a proper map of topological spaces, and of a compact space when the target is a point. Many finiteness results, such as the finiteness of cohomology of coherent sheaves and the existence of the Stein factorization, hold for proper morphisms.
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About this page
| Tag | 9537RKBZPP |
|---|---|
| URI | m2://9537RKBZPP |
| Kind | concept |
| Writing | W0 stub |
| MSC | 14A15 |
| Specializes | Universally closed morphism, Separated morphism |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Abelian variety
- Stein factorization
- Nef line bundle
- Rational singularity
- Abelian scheme
- Semistable reduction theorem
- Grothendieck duality
- Projective morphism
- Resolution of singularities
- Crystalline cohomology
- Borel fixed-point theorem
- Theorem of the cube
- Valuative criterion
- Hilbert scheme