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In this paper, we study profinite descent theory for Picard groups in$K(n)$-local homotopy theory through their inverse limit topology. Buildingupon Burklund's result on the multiplicative structures of generalized Moorespectra, we prove that the module category over a $K(n)$-local commutative ringspectrum is equivalent to the limit of its base changes by a tower ofgeneralized Moore spectra of type $n$. As a result, the $K(n)$-local Picardgroups are endowed with a natural inverse limit topology. This topology allowsus to identify the entire $E_1$ and $E_2$-pages of a descent spectral sequencefor Picard spaces of $K(n)$-local profinite Galois extensions.  Our main examples are $K(n)$-local Picard groups of homotopy fixed points$E_n^{hG}$ of the Morava $E$-theory $E_n$ for all closed subgroups $G$ of theMorava stabilizer group $\mathbb{G}_n$. The $G=\mathbb{G}_n$ case has beenstudied by Heard and Mor. At height $1$, we compute Picard groups of $E_1^{hG}$for all closed subgroups $G$ of $\mathbb{G}_1=\mathbb{Z}_p^\times$ at allprimes as a Mackey functor.

The inverse limit topology and profinite descent on Picard groups in $K(n)$-local homotopy theory