Algebraic geometry Schemes Concept
Noetherian scheme
Summary
A Noetherian scheme is a scheme that is covered by finitely many affine pieces, each the spectrum of a Noetherian ring. It is the finiteness condition under which most of the standard theory of schemes works well. All varieties over a field and all schemes of finite type over are Noetherian.
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About this page
| Tag | ND6XEY68P4 |
|---|---|
| URI | m2://ND6XEY68P4 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 14A15, 13E05 |
| Specializes | Scheme |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Base change theorems
- Ample line bundle
- Stein factorization
- Weil divisor
- Derived category of coherent sheaves
- Regular scheme
- Coherent sheaf
- Grothendieck duality
- Valuative criterion
- Chevalley's theorem on constructible sets
- Generic flatness