Théorie des topos et cohomologie étale des schémas
E884917
Théorie des topos et cohomologie étale des schémas is a foundational multi-volume work in algebraic geometry, originating from Grothendieck’s Séminaire de Géométrie Algébrique, that develops topos theory and étale cohomology of schemes.
All labels observed (4)
How this entity was disambiguated
This entity first appeared as the object of triple T10772789 — 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: Théorie des topos et cohomologie étale des schémas Context triple: [SGA 4, title, Théorie des topos et cohomologie étale des schémas]
-
A.
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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B.
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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C.
Cohomologie Galoisienne
Cohomologie Galoisienne is a foundational monograph by Jean-Pierre Serre that systematically develops Galois cohomology and its deep applications in number theory and algebraic geometry.
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D.
Grothendieck’s scheme-theoretic framework
Grothendieck’s scheme-theoretic framework is a foundational reformulation of algebraic geometry that generalizes varieties using schemes, enabling powerful tools like sheaf theory, cohomology, and modern number-theoretic applications.
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E.
Grothendieck toposes
Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
- 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: Théorie des topos et cohomologie étale des schémas Target entity description: Théorie des topos et cohomologie étale des schémas is a foundational multi-volume work in algebraic geometry, originating from Grothendieck’s Séminaire de Géométrie Algébrique, that develops topos theory and étale cohomology of schemes.
-
A.
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.
-
B.
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.
-
C.
Cohomologie Galoisienne
Cohomologie Galoisienne is a foundational monograph by Jean-Pierre Serre that systematically develops Galois cohomology and its deep applications in number theory and algebraic geometry.
-
D.
Grothendieck’s scheme-theoretic framework
Grothendieck’s scheme-theoretic framework is a foundational reformulation of algebraic geometry that generalizes varieties using schemes, enabling powerful tools like sheaf theory, cohomology, and modern number-theoretic applications.
-
E.
Grothendieck toposes
Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
book series
ⓘ
mathematical monograph ⓘ |
| aim |
generalize sheaf cohomology to Grothendieck topologies
ⓘ
provide foundations for étale cohomology ⓘ |
| alsoKnownAs |
SGA 4
ⓘ
linked to:
SGA
|
| author |
Alexander Grothendieck
ⓘ
Jean-Louis Verdier ⓘ Michel Artin ⓘ
linked to:
Michael Artin
|
| basedOn | Séminaire de Géométrie Algébrique du Bois Marie ⓘ |
| develops |
Grothendieck topos
ⓘ
linked to:
Grothendieck toposes
cohomology of sheaves on a topos ⓘ l-adic sheaves ⓘ étale site of a scheme ⓘ |
| editor |
Luc Illusie
ⓘ
Nick Katz ⓘ Pierre Deligne ⓘ |
| field |
algebraic geometry
ⓘ
category theory ⓘ homological algebra ⓘ number theory ⓘ |
| hasPart |
Volume 1: Théorie des topos
ⓘ
Volume 2: Théorie des topos et cohomologie étale des schémas ⓘ Volume 3: Théorie des topos et cohomologie étale des schémas ⓘ |
| influenced |
Weil conjectures proofs
ⓘ
arithmetic geometry ⓘ modern algebraic geometry ⓘ motivic cohomology ⓘ |
| language | French ⓘ |
| originalPublicationPeriod | 1960s ⓘ |
| partOf | Séminaire de Géométrie Algébrique du Bois Marie (SGA) ⓘ |
| publisher |
Springer-Verlag
ⓘ
linked to:
Springer
|
| relatedWork |
Cohomologie l-adique et fonctions L (SGA 5)
ⓘ
Théorie des intersections et théorème de Riemann–Roch (SGA 6) ⓘ |
| series | Lecture Notes in Mathematics ⓘ |
| subject |
Grothendieck spectral sequence
ⓘ
Grothendieck topologies ⓘ
linked to:
Grothendieck topology
base change theorems ⓘ cohomological dimension ⓘ constructible sheaves ⓘ derived functors ⓘ finiteness theorems in étale cohomology ⓘ l-adic cohomology ⓘ proper base change ⓘ schemes ⓘ sites ⓘ topos theory ⓘ étale cohomology ⓘ |
| volumeCount | 3 ⓘ |
How these facts were elicited
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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: Théorie des topos et cohomologie étale des schémas Description of subject: Théorie des topos et cohomologie étale des schémas is a foundational multi-volume work in algebraic geometry, originating from Grothendieck’s Séminaire de Géométrie Algébrique, that develops topos theory and étale cohomology of schemes.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
Théorie des topos et cohomologie étale des schémas
→
hasPart
→
Volume 2: Théorie des topos et cohomologie étale des schémas
ⓘ
linked to: Théorie des topos et cohomologie étale des schémas
Théorie des topos et cohomologie étale des schémas
→
hasPart
→
Volume 3: Théorie des topos et cohomologie étale des schémas
ⓘ
linked to: Théorie des topos et cohomologie étale des schémas