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.
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.