Oka coherence theorem
E484522
mathematical theorem
result in complex analytic geometry
theorem in complex analysis
theorem in several complex variables
The Oka coherence theorem is a fundamental result in complex analytic geometry stating that the sheaf of germs of holomorphic functions on a complex manifold is coherent, providing a powerful bridge between analytic and algebraic methods.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Oka coherence theorem canonical | 1 |
| Oka theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4996544 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Oka coherence theorem Context triple: [Weierstrass preparation theorem, relatedTo, Oka coherence theorem]
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
B.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
C.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
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D.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
E.
Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining equations.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Oka coherence theorem Target entity description: The Oka coherence theorem is a fundamental result in complex analytic geometry stating that the sheaf of germs of holomorphic functions on a complex manifold is coherent, providing a powerful bridge between analytic and algebraic methods.
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
B.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
C.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
-
D.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
E.
Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining equations.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in complex analytic geometry ⓘ theorem in complex analysis ⓘ theorem in several complex variables ⓘ |
| appliesTo |
complex manifolds
ⓘ
domains in complex Euclidean space ⓘ |
| concerns |
coherent analytic sheaves
ⓘ
germs of holomorphic functions ⓘ sheaves of holomorphic functions ⓘ |
| ensures |
existence of finite presentations for the sheaf of holomorphic functions locally
ⓘ
that kernels of morphisms of finite free analytic sheaves are of finite type ⓘ |
| field |
analytic geometry
ⓘ
complex analysis ⓘ complex analytic geometry ⓘ several complex variables ⓘ sheaf theory ⓘ |
| hasGeneralization | coherence of the structure sheaf of a complex analytic space ⓘ |
| historicalContext | one of the foundational results in the development of several complex variables ⓘ |
| implies |
finiteness of relations among local generators of holomorphic functions
ⓘ
local finite generation of the sheaf of holomorphic functions ⓘ the structure sheaf of a complex manifold is coherent ⓘ |
| importance | fundamental result in complex analytic geometry ⓘ |
| influenced | the development of modern sheaf-theoretic methods in complex analysis ⓘ |
| involvesConcept |
analytic subset
ⓘ
coherent sheaf ⓘ germ of a function ⓘ holomorphic function ⓘ structure sheaf ⓘ |
| mainStatement | the sheaf of germs of holomorphic functions on a complex manifold is coherent ⓘ |
| namedAfter | Kiyoshi Oka ⓘ |
| namedTheoremOf | Kiyoshi Oka ⓘ |
| provides | a bridge between analytic and algebraic methods ⓘ |
| relatedTo |
Cartan theorems A and B
ⓘ
Oka principle ⓘ
linked to:
GAGA principle
Oka–Cartan theory ⓘ coherent sheaf ⓘ |
| status | proved ⓘ |
| strengthenedBy | Cartan theorems A and B ⓘ |
| typeOfCoherence | analytic coherence ⓘ |
| usedIn |
complex analytic geometry
ⓘ
the proof of Cartan theorems A and B ⓘ the study of coherent analytic sheaves ⓘ the theory of analytic spaces ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Oka coherence theorem Description of subject: The Oka coherence theorem is a fundamental result in complex analytic geometry stating that the sheaf of germs of holomorphic functions on a complex manifold is coherent, providing a powerful bridge between analytic and algebraic methods.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Oka coherence theorem