Mathematics – Number Theory
Scientific paper
2004-06-29
Ast\~A\c{opyright}risque 319 (2008), 13--38.
Mathematics
Number Theory
28 pages, in french
Scientific paper
The goal of this article is to show that the following two categories are equivalent (1) the category of filtered (phi,N,G_K)-modules (2) the category of (phi,Gamma_K)-modules over the Robba ring such that the Lie algebra of Gamma_K acts locally trivially. Furthermore, we show that under this equivalence, the admissible filtered (phi,N,G_K)-modules correspond to the etale (phi,Gamma_K)-modules, which gives a new proof of Colmez-Fontaine's theorem.
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