Multivariable (phi,Gamma)-modules and locally analytic vectors

Abstract : Let K_\infty/K be a Galois extension such that K_\infty contains the cyclotomic extension and such that Gamma=Gal(K_\infty/K) is a p-adic Lie group. We construct (phi,Gamma)-modules over the ring of locally analytic vectors (for the action of Gamma) of some of Fontaine's rings. When K_\infty is the cyclotomic extension, these locally analytic vectors are closely related to the Robba ring, and we recover the classical theory. We determine some of these locally analytic vectors in the Lubin-Tate setting. This allows us to prove that a certain monodromy conjecture implies that the Lubin-Tate (phi,Gamma)-modules of F-analytic representations are overconvergent.
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https://hal.archives-ouvertes.fr/hal-00920290
Contributor : Laurent Berger <>
Submitted on : Wednesday, December 18, 2013 - 10:27:43 AM
Last modification on : Thursday, April 4, 2019 - 10:18:04 AM

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  • HAL Id : hal-00920290, version 1
  • ARXIV : 1312.4753

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Laurent Berger. Multivariable (phi,Gamma)-modules and locally analytic vectors. Duke Mathematical Journal, Duke University Press, 2016. ⟨hal-00920290⟩

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