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 (1)
| Label | Occurrences |
|---|---|
| Théorie des topos et cohomologie étale des schémas canonical | 1 |
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.
-
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.
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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.
-
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 NERFINISHED ⓘ |
| author |
Alexander Grothendieck
NERFINISHED
ⓘ
Jean-Louis Verdier NERFINISHED ⓘ Michel Artin NERFINISHED ⓘ |
| basedOn | Séminaire de Géométrie Algébrique du Bois Marie NERFINISHED ⓘ |
| develops |
Grothendieck topos
NERFINISHED
ⓘ
cohomology of sheaves on a topos ⓘ l-adic sheaves ⓘ étale site of a scheme ⓘ |
| editor |
Luc Illusie
NERFINISHED
ⓘ
Nick Katz NERFINISHED ⓘ Pierre Deligne NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ Volume 3: Théorie des topos et cohomologie étale des schémas NERFINISHED ⓘ |
| influenced |
Weil conjectures proofs
ⓘ
arithmetic geometry ⓘ modern algebraic geometry ⓘ motivic cohomology ⓘ |
| language | French ⓘ |
| originalPublicationPeriod | 1960s ⓘ |
| partOf | Séminaire de Géométrie Algébrique du Bois Marie (SGA) NERFINISHED ⓘ |
| publisher | Springer-Verlag NERFINISHED ⓘ |
| relatedWork |
Cohomologie l-adique et fonctions L (SGA 5)
NERFINISHED
ⓘ
Théorie des intersections et théorème de Riemann–Roch (SGA 6) NERFINISHED ⓘ |
| series | Lecture Notes in Mathematics NERFINISHED ⓘ |
| subject |
Grothendieck spectral sequence
NERFINISHED
ⓘ
Grothendieck topologies NERFINISHED ⓘ 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 ⓘ |
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Instruction
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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 (1)
Full triples — surface form annotated when it differs from this entity's canonical label.