Langlands–Tunnell theorem
E1505634
UNEXPLORED
The Langlands–Tunnell theorem is a major result in number theory that proves the modularity of certain two-dimensional Galois representations, playing a key role in progress toward the Taniyama–Shimura–Weil conjecture and Fermat’s Last Theorem.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Langlands–Tunnell theorem canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T21858388 — 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: Langlands–Tunnell theorem Context triple: [Artin’s conjecture on L-functions, specialCaseProvedBy, Langlands–Tunnell theorem]
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A.
Fontaine–Mazur conjecture
The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
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B.
Artin reciprocity law
The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
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C.
Ribet's theorem
Ribet's theorem is a result in number theory that linked certain modular forms to Galois representations and played a crucial role in the proof of Fermat's Last Theorem.
-
D.
Artin’s conjecture on L-functions
Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
-
E.
Chebotarev density theorem
The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
- 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: Langlands–Tunnell theorem Target entity description: The Langlands–Tunnell theorem is a major result in number theory that proves the modularity of certain two-dimensional Galois representations, playing a key role in progress toward the Taniyama–Shimura–Weil conjecture and Fermat’s Last Theorem.
-
A.
Fontaine–Mazur conjecture
The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
-
B.
Artin reciprocity law
The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
-
C.
Ribet's theorem
Ribet's theorem is a result in number theory that linked certain modular forms to Galois representations and played a crucial role in the proof of Fermat's Last Theorem.
-
D.
Artin’s conjecture on L-functions
Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
-
E.
Chebotarev density theorem
The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
- F. None of above. chosen
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.