The Lubin–Tate Iwasawa main conjecture

Let $V$ be a representation for which the $L$-analytic $p$-adic $L$-function $L_p(V)$ is defined, and let $\widetilde{H}^2(V)$ be the Selmer group described above over the $L$-analytic distribution algebra $\Lambda^L_\infty$. Write $\operatorname{char}_{\Lambda^L_\infty}(\widetilde{H}^2(V))$ for its characteristic ideal. Lubin–Tate Iwasawa main conjecture. Under possibly relaxed hypotheses, one should have

$$\operatorname{char}_{\Lambda^L_\infty}\left(\widetilde{H}^2(V)\right)=\left(L_p(V)\right).$$

This is the expected full Iwasawa main conjecture in the $L$-analytic Lubin–Tate setting. The paper describes only a divisibility toward this equality using a constructed element $L_p^*(V)$, while the genuine $p$-adic $L$-function and the full equality remain to be established.