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Main conjecture of Iwasawa theory

In mathematics, the main conjecture of Iwasawa theory is a deep relationship between p-adic L-functions and ideal class groups of cyclotomic fields, proved by Kenkichi Iwasawa for primes satisfying the Kummer–Vandiver conjecture and proved for all primes by Barry Mazur and Andrew Wiles. The Herbrand–Ribet theorem and the Gras conjecture are both easy…

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Conjectured by
Kenkichi Iwasawa
Conjectured in
1969
Field
Algebraic number theory Iwasawa theory
First proof by
Barry Mazur Andrew Wiles
First proof in
1984

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Main conjecture of Iwasawa theory

Nodes54
Edges53
Triples39
Avg. degree1.96
Density0.037037
Components1

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Main conjecture of Iwasawa theory

Top relations

related to Statement · 18
Main conjecture of Iwasawa theory → Bernoulli, Bk, Fn, Gal, Galois, Gp, Hilbert, Hn, Iwasawa, Ln, Ln/Fn, Lp, Mazur, Teichmüller, The, Vi, Wiles, ZpQp
related to history · 15
Main conjecture of Iwasawa theory → Galois, Herbrand, Herbrand's, Iwasawa, Karl Rubin, Ken Ribet's, Kolyvagin's Euler, L-functions, Mazur, Ribet, Thaine's, The, These, This, Wiles
Conjectured by · 1
Main conjecture of Iwasawa theory → Kenkichi Iwasawa
Conjectured in · 1
Main conjecture of Iwasawa theory → 1969
Field · 1
Main conjecture of Iwasawa theory → Algebraic number theory Iwasawa theory
First proof by · 1
Main conjecture of Iwasawa theory → Barry Mazur Andrew Wiles
First proof in · 1
Main conjecture of Iwasawa theory → 1984
is a · 1
Main conjecture of Iwasawa theory → deep relationship between p-adic L-functions and ideal class groups of cyclotomic fields

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Important terminology

conjecture main p-adic iwasawa wiles proved mazur class fields field number theory curve ωi theorem proof function corresponds group galois

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Main conjecture of Iwasawa theoryConjectured byKenkichi Iwasawa1.00infobox
Main conjecture of Iwasawa theoryConjectured in19691.00infobox
Main conjecture of Iwasawa theoryFieldAlgebraic number theory Iwasawa theory1.00infobox
Main conjecture of Iwasawa theoryFirst proof byBarry Mazur Andrew Wiles1.00infobox
Main conjecture of Iwasawa theoryFirst proof in19841.00infobox
Main conjecture of Iwasawa theoryis adeep relationship between p-adic L-functions and ideal class groups of cyclotomic fields0.90text
Main conjecture of Iwasawa theoryrelated to historyThe0.60section
Main conjecture of Iwasawa theoryrelated to historyIwasawa0.60section
Main conjecture of Iwasawa theoryrelated to historyL-functions0.60section
Main conjecture of Iwasawa theoryrelated to historyGalois0.60section
Main conjecture of Iwasawa theoryrelated to historyThis0.60section
Main conjecture of Iwasawa theoryrelated to historyMazur0.60section

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