= One-variable main conjecture for CM elliptic curves
{title2=$\operatorname{char}_\Lambda X_\chi=(\mathcal L_\chi)$}
At a good split prime, the one-prime CM division tower has a pro-$p$ <Galois group> isomorphic to $\mathbb Z_p$. Its prime-ramified <Iwasawa module> is torsion on each finite-character component. The main conjecture identifies its <characteristic ideal> with the corresponding elliptic-unit <p-adic L-function>. The <class-field unit sequence> and equality of characteristic ideals of global-units modulo elliptic-units and of class groups prove the identification. The cyclotomic Selmer formulation requires the appropriate CM twist and two-variable specialization; the one-prime tower is not the cyclotomic tower.
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