Main conjecture of Iwasawa theory | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-31

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Main_conjecture_of_Iwasawa_theory


00:00:46 1 Motivation
00:01:59 2 History
00:03:01 3 Statement



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SUMMARY
=======
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, CM fields, elliptic curves, and so on.