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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 for primes satisfying the Kummer–Vandiver conjecture and proved for all primes by . 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. ==Motivation== was partly motivated by an analogy with Weil's description of the zeta function of an algebraic curve over a finite field in terms of eigenvalues of the Frobenius endomorphism on its Jacobian. In this analogy, *The action of the Frobenius corresponds to the action of the group Γ. *The Jacobian of a curve corresponds to a module ''X'' over Γ defined in terms of ideal class groups *The zeta function of a curve over a finite field corresponds to a ''p''-adic ''L''-function. *Weil's theorem relating the eigenvalues of Frobenius to the zeros of the zeta function of the curve corresponds to Iwasawa's main conjecture relating the action of the Iwasawa algebra on ''X'' to zeros of the ''p''-adic zeta function. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Main conjecture of Iwasawa theory」の詳細全文を読む スポンサード リンク
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