Iwasawa theory
E358023
Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Iwasawa theory canonical | 5 |
How this entity was disambiguated
This entity first appeared as the object of triple T3424532 — 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: Iwasawa theory Context triple: [Karl Rubin, researchArea, Iwasawa theory]
-
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.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
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C.
Hilbert’s twelfth problem
Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
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D.
Dedekind zeta functions
Dedekind zeta functions are number-theoretic functions attached to algebraic number fields that encode their arithmetic properties, such as the distribution of prime ideals and class numbers.
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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: Iwasawa theory Target entity description: Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
-
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.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
-
C.
Hilbert’s twelfth problem
Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
-
D.
Dedekind zeta functions
Dedekind zeta functions are number-theoretic functions attached to algebraic number fields that encode their arithmetic properties, such as the distribution of prime ideals and class numbers.
-
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 (51)
| Predicate | Object |
|---|---|
| instanceOf |
branch of number theory
ⓘ
mathematical theory ⓘ |
| appliesTo |
class groups of number fields
ⓘ
elliptic curves over number fields ⓘ ideal class groups of cyclotomic fields ⓘ modular forms ⓘ motives ⓘ |
| coreConcept |
Selmer group
ⓘ
surface form:
Greenberg Selmer group
Iwasawa algebra ⓘ Iwasawa invariants ⓘ Iwasawa module ⓘ Mazur control theorem ⓘ Selmer group ⓘ Z_p-extension ⓘ control theorem ⓘ cyclotomic Z_p-extension ⓘ lambda invariant ⓘ main conjecture of Iwasawa theory ⓘ mu invariant ⓘ nu invariant ⓘ |
| developedBy |
Kenku Iwasawa
ⓘ
surface form:
Kenkichi Iwasawa
|
| field | number theory ⓘ |
| focusesOn |
Galois groups of infinite pro-p extensions
ⓘ
Z_p-extensions of number fields ⓘ structure of modules over Iwasawa algebras ⓘ |
| furtherDevelopedBy |
Andrew Wiles
ⓘ
Barry Mazur ⓘ Jean-Pierre Serre ⓘ John Coates ⓘ Ralph Greenberg ⓘ |
| namedAfter |
Kenku Iwasawa
ⓘ
surface form:
Kenkichi Iwasawa
Kenku Iwasawa ⓘ |
| relatedTo |
Birch and Swinnerton-Dyer Conjecture
ⓘ
surface form:
Birch and Swinnerton-Dyer conjecture
Bloch–Kato conjecture ⓘ Galois cohomology ⓘ Langlands program ⓘ algebraic number theory ⓘ arithmetic geometry ⓘ p-adic Hodge theory ⓘ |
| studies |
Galois modules
ⓘ
Galois representations ⓘ Selmer groups in towers of number fields ⓘ arithmetic of elliptic curves in towers of fields ⓘ arithmetic of modular forms in towers of fields ⓘ class groups in towers of number fields ⓘ cyclotomic extensions ⓘ growth of arithmetic invariants ⓘ infinite towers of number fields ⓘ p-adic L-functions ⓘ p-primary parts of class groups ⓘ |
| usesMethod | p-adic methods ⓘ |
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: Iwasawa theory Description of subject: Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
cyclotomic field