Taylor–Wiles method
E1487634
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The Taylor–Wiles method is a powerful technique in number theory and arithmetic geometry used to prove modularity lifting theorems, notably enabling the proof of Fermat’s Last Theorem.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Taylor–Wiles method canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T21493977 — 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: Taylor–Wiles method Context triple: [Richard Taylor, knownFor, Taylor–Wiles method]
-
A.
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.
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B.
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.
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C.
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.
-
D.
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.
-
E.
Bloch–Kato conjecture
The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
- 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: Taylor–Wiles method Target entity description: The Taylor–Wiles method is a powerful technique in number theory and arithmetic geometry used to prove modularity lifting theorems, notably enabling the proof of Fermat’s Last Theorem.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
Bloch–Kato conjecture
The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
- F. None of above. chosen
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.