Algebraic geometry Schemes Concept
Smooth morphism
Summary
A smooth morphism of schemes is a flat morphism, locally of finite presentation, whose fibres are smooth schemes over their residue fields. It is the algebraic analogue of a submersion of differentiable manifolds. A variety over a field is smooth exactly when its structure morphism is smooth, and smooth morphisms are stable under composition and base change.
Where this leads
16 pages build on this one.
- Grothendieck–Riemann–Roch theorem
- Canonical bundle
- Abelian scheme
- De Rham cohomology of varieties
- Hirzebruch–Riemann–Roch theorem
- Cubic surface
- Crystalline cohomology
- Serre duality
- Kodaira vanishing theorem
- Generic smoothness
- Adjunction formula
- Kawamata–Viehweg vanishing theorem
- Algebraic stack
- Néron model
- Hodge conjecture
- Étale morphism
Further reading
About this page
| Tag | EXKGG9X6J0 |
|---|---|
| URI | m2://EXKGG9X6J0 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 14A15, 14B25 |
| Specializes | Flat morphism |
| Same as |
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Used by
- Grothendieck–Riemann–Roch theorem
- Canonical bundle
- Abelian scheme
- De Rham cohomology of varieties
- Hirzebruch–Riemann–Roch theorem
- Crystalline cohomology
- Serre duality
- Kodaira vanishing theorem
- Generic smoothness
- Adjunction formula
- Kawamata–Viehweg vanishing theorem
- Algebraic stack
- Néron model
- Hodge conjecture
- Étale morphism