Iwasawa theory and $F$-analytic Lubin-Tate $(\varphi,\Gamma)$-modules

Abstract

Let $K$ be a finite extension of $\mathbf{Q}_p$. We use the theory of $(\varphi,\Gamma)$-modules in the Lubin-Tate setting to construct some corestriction-compatible families of classes in the cohomology of $V$, for certain representations $V$ of $\mathrm{Gal}(\overline{\mathbf{Q}}_p/K)$. 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.