Foundations of Algebraic Geometry
E244836
Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Foundations of Algebraic Geometry canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T2228028 — 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: Foundations of Algebraic Geometry Context triple: [André Weil, notableWork, Foundations of Algebraic Geometry]
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A.
Hodge theory
Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
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B.
Sheaves in Geometry and Logic
Sheaves in Geometry and Logic is a foundational monograph that develops the theory of sheaves and topos theory and explores their deep connections to geometry, logic, and the foundations of mathematics.
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C.
Castelnuovo–Mumford regularity
Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
-
D.
Zariski topology
The Zariski topology is a fundamental topology in algebraic geometry, defined on the spectrum of a ring or an algebraic variety, whose closed sets correspond to solution sets of polynomial equations.
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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: Foundations of Algebraic Geometry Target entity description: Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
-
A.
Hodge theory
Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
-
B.
Sheaves in Geometry and Logic
Sheaves in Geometry and Logic is a foundational monograph that develops the theory of sheaves and topos theory and explores their deep connections to geometry, logic, and the foundations of mathematics.
-
C.
Castelnuovo–Mumford regularity
Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
-
D.
Zariski topology
The Zariski topology is a fundamental topology in algebraic geometry, defined on the spectrum of a ring or an algebraic variety, whose closed sets correspond to solution sets of polynomial equations.
-
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 (29)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
treatise ⓘ |
| aim |
to provide a rigorous foundation for algebraic geometry
ⓘ
to systematize the theory of algebraic varieties ⓘ |
| describedAs |
landmark mathematical treatise
ⓘ
systematic development of modern foundations of algebraic geometry ⓘ |
| field | algebraic geometry ⓘ |
| hasImpactOn |
rigorous foundations of algebraic geometry
ⓘ
systematic development of algebraic geometry ⓘ |
| hasReputationFor | profound influence on algebraic geometry ⓘ |
| influenced |
later textbooks on algebraic geometry
ⓘ
modern treatments of schemes and sheaves in algebraic geometry ⓘ |
| influenceOn | modern algebraic geometry ⓘ |
| language | English ⓘ |
| subjectArea |
commutative algebra
ⓘ
geometry ⓘ pure mathematics ⓘ |
| topic |
birational geometry
ⓘ
coherent sheaves ⓘ cohomology ⓘ dimension theory in algebraic geometry ⓘ divisors ⓘ intersection theory ⓘ line bundles ⓘ morphisms of varieties ⓘ sheaf theory ⓘ varieties ⓘ |
| usedBy |
graduate students in mathematics
ⓘ
researchers in algebraic geometry ⓘ |
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: Foundations of Algebraic Geometry Description of subject: Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
André Weil