# 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.
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Journal articles

https://hal.archives-ouvertes.fr/hal-01255343
Contributor : Marie-Annick Guillemer <>
Submitted on : Wednesday, January 13, 2016 - 2:57:23 PM
Last modification on : Thursday, April 4, 2019 - 10:18:05 AM

### Identifiers

• HAL Id : hal-01255343, version 1
• ARXIV : 1512.03383

### Citation

Laurent Berger, Lionel Fourquaux. Iwasawa theory and $F$-analytic Lubin-Tate $(\varphi,\Gamma)$-modules. Documenta Mathematica, Universität Bielefeld, 2017, 22, pp.999--1030. ⟨hal-01255343⟩

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