Iwasawa Theory and FF-Analytic Lubin-Tate (φ,Γ)(\varphi,\Gamma)-Modules

  • Laurent Berger

    UMPA, ENS de Lyon UMR 5669 du CNRS, Université de Lyon, France
  • Lionel Fourquaux

    IRMAR, UMR 6625 du CNRS, Université Rennes 1, France
Iwasawa Theory and $F$-Analytic Lubin-Tate $(\varphi,\Gamma)$-Modules cover
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Let KK be a finite extension of Qp\bold{Q}p. We use the theory of (φ,Γ)(\varphi,\Gamma)-modules in the Lubin-Tate setting to construct some corestriction-compatible families of classes in the cohomology of VV, for certain representations VV of Gal(Qˉ/K)\mathrm{Gal}(\bold{\bar{Q}}/K). If in addition VV 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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Laurent Berger, Lionel Fourquaux, Iwasawa Theory and FF-Analytic Lubin-Tate (φ,Γ)(\varphi,\Gamma)-Modules. Doc. Math. 22 (2017), pp. 999–1030

DOI 10.4171/DM/585