GAGA theorems
E883480
The GAGA theorems are foundational results in algebraic geometry that rigorously relate complex algebraic varieties to their associated analytic spaces, showing an equivalence between algebraic and analytic categories under suitable conditions.
All labels observed (2)
| Label | Occurrences |
|---|---|
| GAGA theorems canonical | 1 |
| formal GAGA theorems | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10732898 — 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 theorems Context triple: [GAGA (Géométrie Algébrique et Géométrie Analytique), associatedWith, GAGA theorems]
-
A.
Tauberian theorems
Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
-
B.
Szegő limit theorem
The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
-
C.
Montel theorem
Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
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D.
Kesten’s theorem
Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
-
E.
Hadamard three-circle theorem
The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
- 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 theorems Target entity description: The GAGA theorems are foundational results in algebraic geometry that rigorously relate complex algebraic varieties to their associated analytic spaces, showing an equivalence between algebraic and analytic categories under suitable conditions.
-
A.
Tauberian theorems
Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
-
B.
Szegő limit theorem
The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
-
C.
Montel theorem
Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
-
D.
Kesten’s theorem
Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
-
E.
Hadamard three-circle theorem
The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
result in algebraic geometry
ⓘ
theorem family ⓘ |
| acronymFor |
Géométrie Algébrique et Géométrie Analytique
ⓘ
linked to:
Géométrie algébrique et géométrie analytique
|
| appliesTo |
complex projective varieties
ⓘ
proper schemes over the complex numbers ⓘ |
| assumes | proper morphisms over the complex numbers ⓘ |
| author | Jean-Pierre Serre ⓘ |
| baseField | complex numbers ⓘ |
| centralConcept |
analytification functor
ⓘ
coherent algebraic sheaf ⓘ coherent analytic sheaf ⓘ projective morphism ⓘ proper morphism ⓘ |
| concerns | projective varieties over the complex numbers ⓘ |
| context | comparison between algebraic and analytic categories ⓘ |
| establishes | equivalence between algebraic and analytic categories under suitable conditions ⓘ |
| field |
algebraic geometry
ⓘ
complex analytic geometry ⓘ |
| generalizationOf | Chow’s theorem on algebraicity of analytic subvarieties of projective space ⓘ |
| hasConsequence |
algebraicity of analytic subvarieties of projective space
ⓘ
comparison between algebraic and analytic Picard groups for projective complex varieties ⓘ comparison between algebraic and analytic divisor class groups for projective complex varieties ⓘ equivalence of algebraic and analytic line bundles on projective complex varieties ⓘ |
| hasVariant |
GAGA for schemes
ⓘ
formal GAGA theorems ⓘ relative GAGA theorems ⓘ |
| implies |
algebraicity of analytic morphisms between projective complex varieties
ⓘ
equivalence of coherent algebraic sheaves and coherent analytic sheaves on proper complex varieties ⓘ full faithfulness of analytification functor for morphisms of projective complex varieties ⓘ isomorphism between algebraic and analytic cohomology of coherent sheaves on proper complex varieties ⓘ |
| influenced |
comparison results in p-adic geometry
ⓘ
development of modern scheme theory ⓘ non-archimedean analytic geometry ⓘ |
| inspired | later comparison theorems between algebraic and analytic geometry ⓘ |
| language | French ⓘ |
| publicationYear | 1956 ⓘ |
| publishedIn | Annales de l’Institut Fourier ⓘ |
| relates |
complex algebraic varieties
ⓘ
complex analytic spaces ⓘ |
| requires |
Noetherian hypotheses on the algebraic side
ⓘ
finiteness of cohomology for coherent sheaves on proper varieties ⓘ |
| statedIn |
Géométrie Algébrique et Géométrie Analytique
ⓘ
linked to:
Géométrie algébrique et géométrie analytique
|
| status | foundational result in the comparison of algebraic and analytic geometry ⓘ |
| uses |
coherent sheaf theory
ⓘ
projective embeddings ⓘ properness in algebraic geometry ⓘ sheaf cohomology ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: GAGA theorems Description of subject: The GAGA theorems are foundational results in algebraic geometry that rigorously relate complex algebraic varieties to their associated analytic spaces, showing an equivalence between algebraic and analytic categories under suitable conditions.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: GAGA theorems