Sur les courbes algébriques et les variétés qui s’en déduisent
E244839
Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Sur les courbes algébriques et les variétés qui s’en déduisent canonical | 2 |
| André Weil "Variétés abéliennes et courbes algébriques" | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2228031 — 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: Sur les courbes algébriques et les variétés qui s’en déduisent Context triple: [André Weil, notableWork, Sur les courbes algébriques et les variétés qui s’en déduisent]
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A.
Recherches sur les fonctions elliptiques
Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
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B.
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes is a seminal mathematical paper by Niels Henrik Abel that develops fundamental results on transcendental functions and helped lay groundwork for modern analysis.
-
C.
Hilbert’s fourteenth problem
Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
-
D.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
-
E.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
- 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: Sur les courbes algébriques et les variétés qui s’en déduisent Target entity description: Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
-
A.
Recherches sur les fonctions elliptiques
Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
-
B.
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes is a seminal mathematical paper by Niels Henrik Abel that develops fundamental results on transcendental functions and helped lay groundwork for modern analysis.
-
C.
Hilbert’s fourteenth problem
Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
-
D.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
-
E.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics monograph ⓘ work in algebraic geometry ⓘ |
| author | André Weil ⓘ |
| authorBirthYear | 1906 ⓘ |
| authorDeathYear | 1998 ⓘ |
| citedAs | Weil 1948 monograph on algebraic curves and varieties ⓘ |
| contributedTo | foundations of modern algebraic geometry ⓘ |
| field |
algebraic geometry
ⓘ
number theory ⓘ |
| hasAuthorNationality | French ⓘ |
| hasInfluenceOn |
later textbooks in algebraic geometry
ⓘ
research on curves over finite fields ⓘ |
| historicalSignificance |
helped establish modern algebraic geometry
ⓘ
provided early formulation of ideas leading to the Weil conjectures ⓘ |
| influenced |
Grothendieck’s reformulation of algebraic geometry
ⓘ
Weil conjectures ⓘ development of scheme theory ⓘ modern theory of Abelian varieties ⓘ |
| introducedConcept |
Weil cohomological ideas for zeta functions
ⓘ
abstract approach to algebraic curves over arbitrary fields ⓘ |
| language | French ⓘ |
| mathematicalArea |
arithmetic geometry
ⓘ
classical algebraic geometry ⓘ |
| originalTitle | Sur les courbes algébriques et les variétés qui s’en déduisent ⓘ |
| publicationYear | 1948 ⓘ |
| relatedTo |
Riemann hypothesis for curves over finite fields
ⓘ
linked to:
Weil conjectures
Weil conjectures ⓘ zeta function of a curve over a finite field ⓘ |
| topic |
Abelian varieties
ⓘ
Jacobian varieties ⓘ algebraic curves ⓘ algebraic varieties ⓘ divisors on algebraic curves ⓘ function fields of curves ⓘ intersection theory ⓘ rational points on curves ⓘ zeta functions of varieties over finite fields ⓘ |
| usedMethod |
geometric interpretation of number-theoretic problems
ⓘ
intersection-theoretic arguments ⓘ |
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: Sur les courbes algébriques et les variétés qui s’en déduisent Description of subject: Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
Sur les courbes algébriques et les variétés qui s’en déduisent
→
originalTitle
→
Sur les courbes algébriques et les variétés qui s’en déduisent
ⓘ
Mordell–Weil theorem
→
standardReference
→
André Weil "Variétés abéliennes et courbes algébriques"
ⓘ
linked to: Sur les courbes algébriques et les variétés qui s’en déduisent