#### DOCUMENTA MATHEMATICA, Vol. 22 (2017), 999-1030

Laurent Berger and Lionel Fourquaux

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

Let $K$ be a finite extension of $\Qp$. 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 $\Gal(\Qpbar/K)$. 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.

2010 Mathematics Subject Classification: 11F; 11S; 14G

Keywords and Phrases: p-adic representation; (\phi,\Gamma)-module; Lubin-Tate group; overconvergent representation; p-adic Hodge theory; analytic cohomology; normalized traces; Bloch-Kato exponential; Iwasawa theory; Kummer theory

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