Drinfeld modules
E884935
Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Drinfeld modules canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10773429 — 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: Drinfeld modules Context triple: [Vladimir Drinfeld, knownFor, Drinfeld modules]
-
A.
Shimura varieties
Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
-
B.
Galois representations
Galois representations are homomorphisms from Galois groups of field extensions into matrix groups that encode deep arithmetic information and link number theory with algebraic geometry and modular forms.
-
C.
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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D.
Hasse–Weil bound for abelian varieties
The Hasse–Weil bound for abelian varieties is a fundamental result in arithmetic geometry that gives sharp estimates for the number of rational points on abelian varieties over finite fields in terms of their dimension and the field size.
-
E.
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.
- 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: Drinfeld modules Target entity description: Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
-
A.
Shimura varieties
Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
-
B.
Galois representations
Galois representations are homomorphisms from Galois groups of field extensions into matrix groups that encode deep arithmetic information and link number theory with algebraic geometry and modular forms.
-
C.
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.
-
D.
Hasse–Weil bound for abelian varieties
The Hasse–Weil bound for abelian varieties is a fundamental result in arithmetic geometry that gives sharp estimates for the number of rational points on abelian varieties over finite fields in terms of their dimension and the field size.
-
E.
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.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic structure
ⓘ
generalization of elliptic curves ⓘ object in arithmetic geometry ⓘ |
| actOn | additive group via Frobenius-type operators ⓘ |
| centralIn | Drinfeld’s proof of the global Langlands correspondence for GL(2) over function fields ⓘ |
| consideredAs | function field analogues of abelian varieties ⓘ |
| definedOver |
fields of positive characteristic
ⓘ
global function fields ⓘ |
| fieldOfStudy |
arithmetic geometry
ⓘ
function field arithmetic ⓘ number theory ⓘ theory of automorphic forms ⓘ |
| generalizes | elliptic curves over number fields ⓘ |
| hasAnalogueOf |
L-function
ⓘ
Mordell–Weil theorem NERFINISHED ⓘ Néron–Ogg–Shafarevich criterion NERFINISHED ⓘ Serre–Tate theory of deformations NERFINISHED ⓘ Tate module ⓘ complex multiplication theory ⓘ modular forms ⓘ |
| hasComponent |
ring homomorphism from A to endomorphisms of the additive group
ⓘ
underlying additive group scheme ⓘ |
| hasInvariant |
conductor
ⓘ
endomorphism ring ⓘ height ⓘ j-invariant analogue ⓘ |
| hasProperty |
admit a theory of isogenies
ⓘ
admit a theory of torsion points ⓘ admit good and bad reduction at places ⓘ form moduli spaces ⓘ have associated Galois representations ⓘ have associated exponential functions ⓘ have associated periods and quasi-periods ⓘ |
| introducedBy | Vladimir Drinfeld NERFINISHED ⓘ |
| introducedIn | 1970s ⓘ |
| namedAfter | Vladimir Drinfeld NERFINISHED ⓘ |
| oftenAssume | A is a ring of functions regular away from a fixed place of a global function field ⓘ |
| parameterizedBy |
characteristic
ⓘ
rank ⓘ |
| relatedTo |
Anderson motives
NERFINISHED
ⓘ
Drinfeld modular curves NERFINISHED ⓘ Drinfeld modular forms NERFINISHED ⓘ shtukas ⓘ t-motives NERFINISHED ⓘ |
| studiedIn | positive characteristic Hodge theory ⓘ |
| usedIn |
Langlands correspondence over function fields
NERFINISHED
ⓘ
construction of Galois representations ⓘ explicit class field theory for function fields ⓘ study of special values of L-functions ⓘ |
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: Drinfeld modules Description of subject: Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.