GAGA principle
E883478
The GAGA principle is a foundational result in algebraic geometry that establishes a precise correspondence between algebraic geometry over the complex numbers and complex analytic geometry, allowing one to translate problems and results between these two settings.
All labels observed (1)
| Label | Occurrences |
|---|---|
| GAGA principle canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10732884 — 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: GAGA principle Context triple: [GAGA (Géométrie Algébrique et Géométrie Analytique), introducesConcept, GAGA principle]
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A.
Lotus principle
The Lotus principle is a foundational concept in international law asserting that states are free to act as they wish unless explicitly restricted by international law, as articulated in the S.S. Lotus case.
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B.
Lenzsche Regel
Lenzsche Regel ist ein grundlegendes Gesetz der Elektrodynamik, das die Richtung induzierter Ströme so festlegt, dass sie der Ursache ihrer Entstehung entgegenwirken.
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C.
Apollonian principle
The Apollonian principle is Nietzsche’s concept of the rational, orderly, and form-giving impulse in art and human experience, contrasted with the chaotic, ecstatic Dionysian force.
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D.
Lund Principle
The Lund Principle is an ecumenical guideline urging churches to act together in all matters except those in which deep differences of conviction require them to act separately.
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E.
KISS principle
The KISS principle is a design and problem-solving guideline that advocates keeping systems and solutions as simple as possible to improve clarity, reliability, and maintainability.
- 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: GAGA principle Target entity description: The GAGA principle is a foundational result in algebraic geometry that establishes a precise correspondence between algebraic geometry over the complex numbers and complex analytic geometry, allowing one to translate problems and results between these two settings.
-
A.
Lotus principle
The Lotus principle is a foundational concept in international law asserting that states are free to act as they wish unless explicitly restricted by international law, as articulated in the S.S. Lotus case.
-
B.
Lenzsche Regel
Lenzsche Regel ist ein grundlegendes Gesetz der Elektrodynamik, das die Richtung induzierter Ströme so festlegt, dass sie der Ursache ihrer Entstehung entgegenwirken.
-
C.
Apollonian principle
The Apollonian principle is Nietzsche’s concept of the rational, orderly, and form-giving impulse in art and human experience, contrasted with the chaotic, ecstatic Dionysian force.
-
D.
Lund Principle
The Lund Principle is an ecumenical guideline urging churches to act together in all matters except those in which deep differences of conviction require them to act separately.
-
E.
KISS principle
The KISS principle is a design and problem-solving guideline that advocates keeping systems and solutions as simple as possible to improve clarity, reliability, and maintainability.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
equivalence principle
ⓘ
theorem in algebraic geometry ⓘ |
| abbreviationFor | Géométrie Algébrique et Géométrie Analytique NERFINISHED ⓘ |
| aimsTo | translate problems between algebraic and analytic settings ⓘ |
| appliesTo |
complex projective varieties
ⓘ
proper schemes over the complex numbers ⓘ |
| asserts |
every analytic coherent sheaf on a proper complex algebraic variety is algebraizable
ⓘ
every analytic morphism between proper complex algebraic varieties is algebraic ⓘ isomorphism between algebraic and analytic cohomology of coherent sheaves ⓘ |
| baseField | complex numbers ⓘ |
| compares |
algebraic category of coherent sheaves
ⓘ
analytic category of coherent sheaves ⓘ |
| concerns |
cohomology of coherent sheaves
ⓘ
proper morphisms over the complex numbers ⓘ |
| context |
complex analytic spaces
ⓘ
proper complex algebraic varieties ⓘ |
| ensures | analytic invariants coincide with algebraic invariants for proper complex varieties ⓘ |
| establishes |
equivalence between algebraic and analytic coherent sheaves
ⓘ
equivalence between algebraic and analytic line bundles ⓘ equivalence between algebraic and analytic vector bundles ⓘ |
| field |
algebraic geometry
ⓘ
complex analytic geometry ⓘ |
| formulatedBy | Jean-Pierre Serre NERFINISHED ⓘ |
| generalizedBy |
formal GAGA theorems
NERFINISHED
ⓘ
non-archimedean GAGA theorems ⓘ rigid-analytic GAGA theorems NERFINISHED ⓘ |
| hasAbbreviation | GAGA ⓘ |
| implies |
equivalence of categories of algebraic and analytic line bundles on proper complex varieties
ⓘ
equivalence of categories of algebraic and analytic vector bundles on proper complex varieties ⓘ equivalence of categories of coherent algebraic and analytic sheaves on proper complex varieties ⓘ |
| influenced |
development of comparison theorems in algebraic geometry
ⓘ
modern theory of schemes ⓘ |
| language |
category theory
ⓘ
sheaf cohomology ⓘ |
| publicationYear | 1956 ⓘ |
| publishedIn | Annales de l’Institut Fourier NERFINISHED ⓘ |
| relatedTo |
Riemann existence theorem
NERFINISHED
ⓘ
Serre’s cohomology theorems NERFINISHED ⓘ comparison theorems between algebraic and analytic geometry ⓘ |
| relates |
algebraic geometry over the complex numbers
ⓘ
complex analytic geometry ⓘ |
| statedIn | Géométrie Algébrique et Géométrie Analytique NERFINISHED ⓘ |
| uses | analytification functor ⓘ |
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: GAGA principle Description of subject: The GAGA principle is a foundational result in algebraic geometry that establishes a precise correspondence between algebraic geometry over the complex numbers and complex analytic geometry, allowing one to translate problems and results between these two settings.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.