= Iwasawa main conjecture
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{wiki=Main_conjecture_of_Iwasawa_theory}
The classical Iwasawa main conjecture, now a theorem over $\mathbb Q$, identifies characteristic ideals of appropriate cyclotomic <Iwasawa modules> with ideals generated by <p-adic L-function> power series. For a nontrivial even character in the p-ramified convention, $\operatorname{char}_\Lambda X_\chi=(g_\chi)$ with $g_\chi((1+p)^{1-s}-1)=L_p(\chi,s)$. The <Kummer reflection in Iwasawa theory> accounts for the reflected odd class-group convention.
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