Théorie des intersections et théorème de Riemann–Roch
E886195
"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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Théorie des intersections et théorème de Riemann–Roch canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10772798 — 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 intersections et théorème de Riemann–Roch Context triple: [SGA 6, title, Théorie des intersections et théorème de Riemann–Roch]
-
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.
Sur les courbes algébriques et les variétés qui s’en déduisent
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.
-
C.
Serre’s cohomological methods in algebraic geometry
Serre’s cohomological methods in algebraic geometry are foundational techniques that use sheaf cohomology to relate and study algebraic and analytic geometry, profoundly influencing modern algebraic geometry and complex geometry.
-
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.
Grothendieck–Ogg–Shafarevich formula
The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
- 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 intersections et théorème de Riemann–Roch Target entity description: "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.
-
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.
Sur les courbes algébriques et les variétés qui s’en déduisent
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.
-
C.
Serre’s cohomological methods in algebraic geometry
Serre’s cohomological methods in algebraic geometry are foundational techniques that use sheaf cohomology to relate and study algebraic and analytic geometry, profoundly influencing modern algebraic geometry and complex geometry.
-
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.
Grothendieck–Ogg–Shafarevich formula
The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
SGA volume
ⓘ
mathematics book ⓘ seminar proceedings ⓘ |
| abbreviation | SGA 6 NERFINISHED ⓘ |
| appliesTo |
proper morphisms of schemes
ⓘ
schemes ⓘ |
| author | Alexander Grothendieck NERFINISHED ⓘ |
| basedOn | Grothendieck’s seminars at IHÉS NERFINISHED ⓘ |
| contains |
construction of Chern classes in K-theory
ⓘ
exposition of Grothendieck–Riemann–Roch in generality ⓘ formalism of operations on Chow groups ⓘ |
| countryOfOrigin | France ⓘ |
| develops | foundations of intersection theory in algebraic geometry ⓘ |
| editor |
Alexander Grothendieck
NERFINISHED
ⓘ
Luc Illusie NERFINISHED ⓘ Pierre Berthelot NERFINISHED ⓘ |
| establishes | general form of the Riemann–Roch theorem ⓘ |
| field | algebraic geometry ⓘ |
| focusesOn |
Riemann–Roch theorem
NERFINISHED
ⓘ
intersection theory ⓘ |
| hasFormat |
digital PDF
ⓘ
printed book ⓘ |
| influenced |
Fulton’s Intersection Theory
NERFINISHED
ⓘ
development of algebraic K-theory ⓘ modern intersection theory ⓘ |
| institution | IHÉS NERFINISHED ⓘ |
| language | French ⓘ |
| LNMNumber | 225 ⓘ |
| originalSeminarYears | 1966–1967 GENERATED ⓘ |
| partOf | Séminaire de Géométrie Algébrique du Bois Marie NERFINISHED ⓘ |
| publicationYear | 1971 ⓘ |
| publisher | Springer-Verlag NERFINISHED ⓘ |
| relatedTo |
SGA 5
NERFINISHED
ⓘ
SGA 7 NERFINISHED ⓘ Éléments de géométrie algébrique NERFINISHED ⓘ |
| series | Lecture Notes in Mathematics NERFINISHED ⓘ |
| subject |
Chern classes
ⓘ
Chow groups ⓘ Grothendieck groups NERFINISHED ⓘ Grothendieck–Riemann–Roch theorem NERFINISHED ⓘ K-theory NERFINISHED ⓘ Riemann–Roch for higher-dimensional varieties NERFINISHED ⓘ coherent sheaves ⓘ cycle classes ⓘ derived functors in algebraic geometry ⓘ functoriality of Riemann–Roch ⓘ proper morphisms of schemes ⓘ |
| title | Théorie des intersections et théorème de Riemann–Roch NERFINISHED ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Théorie des intersections et théorème de Riemann–Roch Description of subject: "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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.