Weil–Deligne representations
E1495487
UNEXPLORED
Weil–Deligne representations are algebraic objects combining a representation of the Weil group with a nilpotent operator, used to describe local Galois representations and formulate the local Langlands correspondence.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Weil–Deligne parameter | 1 |
| Weil–Deligne representation | 1 |
| Weil–Deligne representation of a local field | 1 |
| Weil–Deligne representations canonical | 1 |
| local Langlands correspondence | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T21654192 — 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: Weil–Deligne representations Context triple: [Galois representations, relatedTo, Weil–Deligne representations]
-
A.
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.
-
B.
Serre’s conjecture on Galois representations
Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
-
C.
Mazur's deformation theory of Galois representations
Mazur's deformation theory of Galois representations is a foundational framework in number theory that systematically studies how p-adic Galois representations can be deformed, with deep applications to modular forms and the proof of Fermat’s Last Theorem.
-
D.
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.
-
E.
Automorphic Forms and the Reciprocity Law
"Automorphic Forms and the Reciprocity Law" is a seminal mathematical work by Goro Shimura that develops deep connections between automorphic forms, number theory, and reciprocity laws in 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: Weil–Deligne representations Target entity description: Weil–Deligne representations are algebraic objects combining a representation of the Weil group with a nilpotent operator, used to describe local Galois representations and formulate the local Langlands correspondence.
-
A.
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.
-
B.
Serre’s conjecture on Galois representations
Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
-
C.
Mazur's deformation theory of Galois representations
Mazur's deformation theory of Galois representations is a foundational framework in number theory that systematically studies how p-adic Galois representations can be deformed, with deep applications to modular forms and the proof of Fermat’s Last Theorem.
-
D.
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.
-
E.
Automorphic Forms and the Reciprocity Law
"Automorphic Forms and the Reciprocity Law" is a seminal mathematical work by Goro Shimura that develops deep connections between automorphic forms, number theory, and reciprocity laws in arithmetic geometry.
- F. None of above. chosen
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Weil–Deligne representations
linked to: Weil–Deligne representations
linked to: Weil–Deligne representations
linked to: Weil–Deligne representations