Field | Algebraic number theory Iwasawa theory |
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Conjectured by | Kenkichi Iwasawa |
Conjectured in | 1969 |
First proof by | Barry Mazur Andrew Wiles |
First proof in | 1984 |
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 Mazur and Wiles (1984). The Herbrand–Ribet theorem and the Gras conjecture are both easy consequences of the main conjecture. There are several generalizations of the main conjecture, to totally real fields,[1] CM fields, elliptic curves, and so on.