Bruhat–Tits theory
E921613
Bruhat–Tits theory is a framework in arithmetic geometry and representation theory that studies reductive algebraic groups over non-archimedean local fields via associated geometric objects called Bruhat–Tits buildings.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Bruhat–Tits buildings | 1 |
| Bruhat–Tits theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11365357 — 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: Bruhat–Tits theory Context triple: [Deligne–Lusztig theory, relatesTo, Bruhat–Tits theory]
-
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.
Real Reductive Groups II
Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
-
C.
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.
-
D.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
-
E.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
- 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: Bruhat–Tits theory Target entity description: Bruhat–Tits theory is a framework in arithmetic geometry and representation theory that studies reductive algebraic groups over non-archimedean local fields via associated geometric objects called Bruhat–Tits buildings.
-
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.
Real Reductive Groups II
Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
-
C.
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.
-
D.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
-
E.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theory
ⓘ
theory in arithmetic geometry ⓘ theory in representation theory ⓘ |
| appliesTo |
reductive groups over non-archimedean local fields
ⓘ
reductive groups over p-adic fields ⓘ |
| assumes | non-archimedean local field with discrete valuation ⓘ |
| basedOn |
Tits theory of buildings
ⓘ
structure theory of reductive algebraic groups ⓘ |
| characteristicOf | non-archimedean geometry ⓘ |
| developedIn | 1970s ⓘ |
| field |
algebraic groups
ⓘ
arithmetic geometry ⓘ p-adic groups ⓘ representation theory ⓘ |
| hasApplication |
construction of local factors in the Langlands correspondence
ⓘ
study of reduction of algebraic groups modulo the maximal ideal of the valuation ring ⓘ |
| hasPart |
classification of parahoric subgroups
ⓘ
construction of buildings from valued root data ⓘ description of special and hyperspecial vertices ⓘ |
| influenced |
Moy–Prasad theory
ⓘ
theory of buildings in geometric group theory ⓘ |
| mainSubject | reductive algebraic groups over non-archimedean local fields ⓘ |
| namedAfter |
François Bruhat
ⓘ
Jacques Tits ⓘ |
| provides |
classification of reductive groups over non-archimedean local fields up to isomorphism
ⓘ
construction of Bruhat–Tits buildings attached to reductive groups ⓘ description of maximal compact subgroups via vertices in buildings ⓘ description of parahoric subgroups via facets in buildings ⓘ structure theory for p-adic groups ⓘ |
| relates |
algebraic structure of a reductive group
ⓘ
geometry of its associated building ⓘ |
| studies |
Moy–Prasad filtrations (via its later developments)
ⓘ
filtrations of parahoric subgroups ⓘ group schemes over valuation rings ⓘ integral models of reductive groups ⓘ |
| usedIn |
construction of types and Hecke algebras for p-adic groups
ⓘ
harmonic analysis on p-adic groups ⓘ local aspects of the Langlands program ⓘ representation theory of p-adic groups ⓘ study of automorphic forms ⓘ |
| usesConcept |
Bruhat–Tits buildings
ⓘ
linked to:
Bruhat–Tits theory
affine buildings ⓘ apartment ⓘ chamber ⓘ maximal compact subgroups ⓘ parahoric subgroups ⓘ root data ⓘ valuations of root data ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Bruhat–Tits theory Description of subject: Bruhat–Tits theory is a framework in arithmetic geometry and representation theory that studies reductive algebraic groups over non-archimedean local fields via associated geometric objects called Bruhat–Tits buildings.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Bruhat–Tits theory