EGA III
E883475
EGA III is a foundational volume of Grothendieck and Dieudonné’s Éléments de Géométrie Algébrique that develops cohomology theory for schemes, including the formulation of Serre duality in the language of modern algebraic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| EGA III canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T10732824 — 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: EGA III Context triple: [Serre duality, appearsIn, EGA III]
-
A.
Mark III
Mark III is one of Tony Stark’s early Iron Man armor suits, recognized for refining his initial design into a more advanced, weaponized, and iconic red-and-gold configuration.
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B.
G3
G3 is the IATA airline designator assigned to the Brazilian low-cost carrier GOL Linhas Aéreas Inteligentes.
-
C.
G3
G3 is a recurring concert tour and project that brings together virtuoso rock guitarists, founded by Joe Satriani and featuring rotating lineups of top players.
-
D.
Este III
Este III is an archaeological phase of the Este culture in northern Italy, marked by its characteristic Iron Age material culture and settlement patterns.
-
E.
GA-03
GA-03 is the abbreviated designation for Georgia's 3rd congressional district, a U.S. House of Representatives district located in western Georgia.
- 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: EGA III Target entity description: EGA III is a foundational volume of Grothendieck and Dieudonné’s Éléments de Géométrie Algébrique that develops cohomology theory for schemes, including the formulation of Serre duality in the language of modern algebraic geometry.
-
A.
Mark III
Mark III is one of Tony Stark’s early Iron Man armor suits, recognized for refining his initial design into a more advanced, weaponized, and iconic red-and-gold configuration.
-
B.
G3
G3 is the IATA airline designator assigned to the Brazilian low-cost carrier GOL Linhas Aéreas Inteligentes.
-
C.
G3
G3 is a recurring concert tour and project that brings together virtuoso rock guitarists, founded by Joe Satriani and featuring rotating lineups of top players.
-
D.
Este III
Este III is an archaeological phase of the Este culture in northern Italy, marked by its characteristic Iron Age material culture and settlement patterns.
-
E.
GA-03
GA-03 is the abbreviated designation for Georgia's 3rd congressional district, a U.S. House of Representatives district located in western Georgia.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
research monograph ⓘ volume of Éléments de Géométrie Algébrique ⓘ |
| aim | to provide a general cohomological framework for schemes ⓘ |
| author |
Alexander Grothendieck
NERFINISHED
ⓘ
Jean Dieudonné NERFINISHED ⓘ |
| contribution |
develops general base change theorems for cohomology
ⓘ
establishes general cohomology theory for proper morphisms of schemes ⓘ proves finiteness of higher direct images of coherent sheaves under proper morphisms ⓘ reformulates classical Serre duality using schemes and coherent sheaves ⓘ systematizes cohomological tools for algebraic geometry ⓘ |
| field | algebraic geometry ⓘ |
| follows | EGA II NERFINISHED ⓘ |
| framework | scheme theory ⓘ |
| hasCanonicalAbbreviation | EGA III NERFINISHED ⓘ |
| hasPart |
EGA III extsubscript{1}
ⓘ
EGA III extsubscript{2} ⓘ |
| influenced |
Grothendieck’s theory of schemes in SGA
ⓘ
development of duality theory in algebraic geometry ⓘ modern scheme-theoretic algebraic geometry ⓘ |
| inSeries | Publications Mathématiques de l’IHÉS NERFINISHED ⓘ |
| language | French ⓘ |
| mathematicalSubjectClassification |
14-XX
ⓘ
14Fxx ⓘ |
| originalTitle | Éléments de Géométrie Algébrique III NERFINISHED ⓘ |
| partOf | Éléments de Géométrie Algébrique NERFINISHED ⓘ |
| precedes | EGA IV NERFINISHED ⓘ |
| seriesNumber | III ⓘ |
| subjectOf | Serre duality in the language of schemes ⓘ |
| topic |
Grothendieck’s formalism of derived functors (at the level of δ-functors)
ⓘ
Serre duality NERFINISHED ⓘ base change in cohomology ⓘ coherent sheaf cohomology ⓘ cohomological dimension ⓘ cohomology of schemes ⓘ direct images of coherent sheaves ⓘ finiteness theorems ⓘ proper morphisms of schemes ⓘ |
| usesConcept |
Noetherian schemes
NERFINISHED
ⓘ
coherent sheaves ⓘ proper morphism ⓘ sheaf cohomology ⓘ |
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: EGA III Description of subject: EGA III is a foundational volume of Grothendieck and Dieudonné’s Éléments de Géométrie Algébrique that develops cohomology theory for schemes, including the formulation of Serre duality in the language of modern algebraic geometry.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.