The canonical map W(k_{K_∞})[[μ]] → A_K ∩ A_inf is an isomorphism, even if K is ramified.
Le corps des normes de certaines extensions infinies de corps locaux; applications
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A remark on an integral structure of the imperfect coefficient ring of $(\varphi,\Gamma)$-modules
The canonical map W(k_{K_∞})[[μ]] → A_K ∩ A_inf is an isomorphism, even if K is ramified.