Szpiro conjecture
E1487645
UNEXPLORED
The Szpiro conjecture is a deep unproven statement in arithmetic geometry about the relationship between the discriminant and conductor of elliptic curves over the rationals, and is known to be essentially equivalent to the abc conjecture.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Masser–Oesterlé conjecture | 2 |
| Oesterlé–Masser conjecture | 1 |
| Szpiro conjecture canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T21494131 — 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: Szpiro conjecture Context triple: [abc conjecture, relatedTo, Szpiro conjecture]
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A.
Bombieri–Lang conjecture
The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
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B.
Birch and Swinnerton-Dyer Conjecture
The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
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C.
Faltings' theorem
Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
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D.
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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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: Szpiro conjecture Target entity description: The Szpiro conjecture is a deep unproven statement in arithmetic geometry about the relationship between the discriminant and conductor of elliptic curves over the rationals, and is known to be essentially equivalent to the abc conjecture.
-
A.
Bombieri–Lang conjecture
The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
-
B.
Birch and Swinnerton-Dyer Conjecture
The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
-
C.
Faltings' theorem
Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
-
D.
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.
-
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 (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Szpiro conjecture
linked to: Szpiro conjecture
linked to: Szpiro conjecture