= Kummer reflection in Iwasawa theory
{c}
{title2=$X_\chi\sim Y_{\omega\chi^{-1}}^\iota(1)$}
For nontrivial even $\chi$ in the full cyclotomic tower of $\mathbb Q$, <Kummer theory> relates the <p-ramified Iwasawa module> to the reflected odd <unramified Iwasawa module>, up to <pseudo-isomorphism>. Here $\iota(\gamma)=\gamma^{-1}$ and $(1)$ is the <Tate twist>. The induced substitution on characteristic series is $T\mapsto u(1+T)^{-1}-1$, where $u$ is the cyclotomic value of $\gamma$. Omitting either operation changes the interpolation convention.
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