Iwasawa Theory and $F$-Analytic Lubin-Tate $(\phi ,\Gamma )$-Modules

Abstract

Let $K$ be a finite extension of $\mathbf{Q}p$. We use the theory of $(\phi ,\Gamma )$-modules in the Lubin-Tate setting to construct some corestriction-compatible families of classes in the cohomology of $V$, for certain representations $V$ of $\mathrm{Gal}(\bar{\mathbf{Q}}/K)$. If in addition $V$ is crystalline, we describe these classes explicitly using Bloch-Kato's exponential maps. This allows us to generalize Perrin-Riou's period map to the Lubin-Tate setting.