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 |
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 ⓘ |
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
cyclotomic field