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 (1)
| Label | Occurrences |
|---|---|
| Oka coherence theorem canonical | 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.
-
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 NERFINISHED ⓘ |
| namedTheoremOf | Kiyoshi Oka NERFINISHED ⓘ |
| provides | a bridge between analytic and algebraic methods ⓘ |
| relatedTo |
Cartan theorems A and B
NERFINISHED
ⓘ
Oka principle NERFINISHED ⓘ Oka–Cartan theory NERFINISHED ⓘ coherent sheaf ⓘ |
| status | proved ⓘ |
| strengthenedBy | Cartan theorems A and B NERFINISHED ⓘ |
| 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
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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 (1)
Full triples — surface form annotated when it differs from this entity's canonical label.