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 $\mathrm{Gal}({\overline{\mathbf{Q}}}_p/K)$. 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.

v2: final version, to appear in Documenta Mathematica. 31 pages