FGA (Fondements de la géométrie algébrique)
E886802
FGA (Fondements de la géométrie algébrique) is a foundational collection of Alexander Grothendieck’s seminar expositions that systematically developed modern algebraic geometry, including major results such as the Grothendieck–Riemann–Roch theorem.
All labels observed (2)
| Label | Occurrences |
|---|---|
| FGA (Fondements de la géométrie algébrique) canonical | 1 |
| Fondements de la géométrie algébrique | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10772698 — 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: FGA (Fondements de la géométrie algébrique) Context triple: [Grothendieck–Riemann–Roch theorem, appearsIn, FGA (Fondements de la géométrie algébrique)]
-
A.
GAGA (Géométrie Algébrique et Géométrie Analytique)
GAGA (Géométrie Algébrique et Géométrie Analytique) is Jean-Pierre Serre’s foundational 1956 paper establishing deep equivalences between algebraic geometry and complex analytic geometry, particularly for projective varieties.
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B.
Éléments de géométrie algébrique
Éléments de géométrie algébrique is a foundational multi-volume treatise that reshaped modern algebraic geometry by developing the theory of schemes and cohomology in a highly general, abstract framework.
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C.
Séminaire de Géométrie Algébrique du Bois Marie
Séminaire de Géométrie Algébrique du Bois Marie is a foundational multi-volume series of advanced seminars that reshaped modern algebraic geometry through the development of schemes, cohomology theories, and the Grothendieck school’s methods.
-
D.
L’Analysis Situs et la Géométrie Algébrique
L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
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E.
Théorie des intersections et théorème de Riemann–Roch
"Théorie des intersections et théorème de Riemann–Roch" is a volume of the Séminaire de Géométrie Algébrique (SGA 6) that develops the foundations of intersection theory in algebraic geometry and establishes a general form of the Riemann–Roch theorem.
- 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: FGA (Fondements de la géométrie algébrique) Target entity description: FGA (Fondements de la géométrie algébrique) is a foundational collection of Alexander Grothendieck’s seminar expositions that systematically developed modern algebraic geometry, including major results such as the Grothendieck–Riemann–Roch theorem.
-
A.
GAGA (Géométrie Algébrique et Géométrie Analytique)
GAGA (Géométrie Algébrique et Géométrie Analytique) is Jean-Pierre Serre’s foundational 1956 paper establishing deep equivalences between algebraic geometry and complex analytic geometry, particularly for projective varieties.
-
B.
Éléments de géométrie algébrique
Éléments de géométrie algébrique is a foundational multi-volume treatise that reshaped modern algebraic geometry by developing the theory of schemes and cohomology in a highly general, abstract framework.
-
C.
Séminaire de Géométrie Algébrique du Bois Marie
Séminaire de Géométrie Algébrique du Bois Marie is a foundational multi-volume series of advanced seminars that reshaped modern algebraic geometry through the development of schemes, cohomology theories, and the Grothendieck school’s methods.
-
D.
L’Analysis Situs et la Géométrie Algébrique
L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
-
E.
Théorie des intersections et théorème de Riemann–Roch
"Théorie des intersections et théorème de Riemann–Roch" is a volume of the Séminaire de Géométrie Algébrique (SGA 6) that develops the foundations of intersection theory in algebraic geometry and establishes a general form of the Riemann–Roch theorem.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical text
ⓘ
seminar proceedings ⓘ work in algebraic geometry ⓘ |
| abbreviation | FGA ⓘ |
| author | Alexander Grothendieck ⓘ |
| containsResult |
Grothendieck–Riemann–Roch theorem
ⓘ
Grothendieck’s formulation of the Riemann–Roch theorem ⓘ existence of fibered products in schemes ⓘ foundations of the theory of Hilbert schemes ⓘ foundations of the theory of Picard schemes ⓘ foundations of the theory of algebraic spaces ⓘ foundations of the theory of base change ⓘ foundations of the theory of coherent sheaves ⓘ foundations of the theory of descent ⓘ foundations of the theory of direct images ⓘ foundations of the theory of formal schemes ⓘ foundations of the theory of inverse images ⓘ foundations of the theory of moduli functors ⓘ
linked to:
Grothendieck’s representability theorem
foundations of the theory of morphisms of schemes ⓘ foundations of the theory of representable functors ⓘ foundations of the theory of schemes ⓘ
linked to:
Foundations of Algebraic Geometry
relative point of view in algebraic geometry ⓘ theory of flatness in algebraic geometry ⓘ use of categories and functors in algebraic geometry ⓘ |
| develops |
functorial viewpoint in algebraic geometry
ⓘ
relative viewpoint in algebraic geometry ⓘ |
| field | algebraic geometry ⓘ |
| hasAuthor | Alexander Grothendieck ⓘ |
| influenced |
modern scheme-theoretic algebraic geometry
ⓘ
Éléments de géométrie algébrique ⓘ |
| isFoundationFor |
Grothendieck school of algebraic geometry
ⓘ
linked to:
Grothendieck’s scheme-theoretic framework
|
| language | French ⓘ |
| period | 20th-century mathematics ⓘ |
| title |
Fondements de la géométrie algébrique
ⓘ
linked to:
FGA (Fondements de la géométrie algébrique)
|
| topic |
Hilbert schemes
ⓘ
linked to:
Hilbert scheme theory
Picard schemes ⓘ
linked to:
Picard scheme
algebraic spaces ⓘ base change ⓘ coherent sheaves ⓘ descent theory ⓘ direct image functors ⓘ flat morphisms ⓘ formal schemes ⓘ inverse image functors ⓘ moduli problems ⓘ representable functors ⓘ schemes ⓘ |
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: FGA (Fondements de la géométrie algébrique) Description of subject: FGA (Fondements de la géométrie algébrique) is a foundational collection of Alexander Grothendieck’s seminar expositions that systematically developed modern algebraic geometry, including major results such as the Grothendieck–Riemann–Roch theorem.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: FGA (Fondements de la géométrie algébrique)