Beilinson–Drinfeld Grassmannian
E876105
The Beilinson–Drinfeld Grassmannian is a geometric object in algebraic geometry and representation theory that generalizes the affine Grassmannian to configurations of multiple points, playing a central role in the geometric Langlands program.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Beilinson–Drinfeld Grassmannian canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10617349 — 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: Beilinson–Drinfeld Grassmannian Context triple: [Alexander Beilinson, knownFor, Beilinson–Drinfeld Grassmannian]
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A.
Deligne–Lusztig theory
Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
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B.
Kazhdan–Lusztig theory
Kazhdan–Lusztig theory is a framework in representation theory and algebraic geometry that studies Hecke algebras and their bases via Kazhdan–Lusztig polynomials, with deep connections to the representation theory of Lie algebras and geometry of Schubert varieties.
-
C.
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.
-
D.
Gerbes
Gerbes is a regional supermarket chain in the United States operating as a banner of Kroger and offering groceries and household goods.
-
E.
Adeles and Algebraic Groups
"Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
- 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: Beilinson–Drinfeld Grassmannian Target entity description: The Beilinson–Drinfeld Grassmannian is a geometric object in algebraic geometry and representation theory that generalizes the affine Grassmannian to configurations of multiple points, playing a central role in the geometric Langlands program.
-
A.
Deligne–Lusztig theory
Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
-
B.
Kazhdan–Lusztig theory
Kazhdan–Lusztig theory is a framework in representation theory and algebraic geometry that studies Hecke algebras and their bases via Kazhdan–Lusztig polynomials, with deep connections to the representation theory of Lie algebras and geometry of Schubert varieties.
-
C.
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.
-
D.
Gerbes
Gerbes is a regional supermarket chain in the United States operating as a banner of Kroger and offering groceries and household goods.
-
E.
Adeles and Algebraic Groups
"Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
geometric object
ⓘ
ind-scheme ⓘ moduli space ⓘ |
| alternativeName | BD Grassmannian NERFINISHED ⓘ |
| appearsIn | Beilinson–Drinfeld formulation of geometric Langlands NERFINISHED ⓘ |
| builtOver | Ran space of the curve ⓘ |
| categoryOfSheavesOn | tensor category equivalent to representations of Langlands dual group (via geometric Satake) ⓘ |
| centralRoleIn | geometric Langlands program NERFINISHED ⓘ |
| constructedFor | connected reductive group G ⓘ |
| definedFor | reductive algebraic group ⓘ |
| definedOver | algebraic curve ⓘ |
| dependsOn |
choice of reductive group G
ⓘ
choice of smooth projective curve ⓘ |
| encodes |
fusion (convolution) product of perverse sheaves
ⓘ
tensor product structure on representations via geometric Satake ⓘ |
| fiberIs |
affine Grassmannian when all points coincide
ⓘ
product of affine Grassmannians when points are distinct ⓘ |
| fiberOver | configuration of points on a curve ⓘ |
| field |
algebraic geometry
ⓘ
representation theory ⓘ |
| generalizes | affine Grassmannian NERFINISHED ⓘ |
| hasBase | configuration space of points on a curve ⓘ |
| hasLocalModel | affine Grassmannian at each point ⓘ |
| hasProperty | compatible with collisions of points ⓘ |
| hasStructure |
factorization space
ⓘ
ind-projective scheme (in many cases) ⓘ |
| namedAfter |
Alexander Beilinson
NERFINISHED
ⓘ
Vladimir Drinfeld NERFINISHED ⓘ |
| parameterizes | G-bundles on a curve with modifications at several points ⓘ |
| relatedConcept |
Ran space of a curve
ⓘ
chiral homology ⓘ factorization algebra ⓘ |
| relatedTo |
affine Kac–Moody algebras
NERFINISHED
ⓘ
geometric Langlands program NERFINISHED ⓘ loop group of a reductive group ⓘ moduli of G-bundles on algebraic curves ⓘ |
| supports |
D-modules
ⓘ
perverse sheaves ⓘ |
| usedBy |
Alexander Beilinson
NERFINISHED
ⓘ
Dennis Gaitsgory NERFINISHED ⓘ Vladimir Drinfeld NERFINISHED ⓘ |
| usedFor |
construction of Hecke eigensheaves
ⓘ
construction of chiral algebras ⓘ construction of vertex algebras in geometric representation theory ⓘ definition of geometric Hecke operators ⓘ factorization structures in geometric representation theory ⓘ |
| usedIn | geometric Satake equivalence NERFINISHED ⓘ |
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: Beilinson–Drinfeld Grassmannian Description of subject: The Beilinson–Drinfeld Grassmannian is a geometric object in algebraic geometry and representation theory that generalizes the affine Grassmannian to configurations of multiple points, playing a central role in the geometric Langlands program.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.