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Représentations p-adiques. (French) Zbl 0575.14038
Proc. Int. Congr. Math., Warszawa 1983, Vol. 1, 475-486 (1984).
[For the entire collection see Zbl 0553.00001.]
This paper is devoted to p-adic representations, i.e. representations of the Galois group G of a local field K, char K\(=0\), in a finite- dimensional vector space over \({\mathbb{Q}}_ p\). The following issues are considered:
1. Unramified representations which are shown to be equivalent to Dieudonné modules of zero slope. - 2. A description of p-adic representations in terms of ”\(\Gamma\)-Dieudonné modules of zero slope”, where \(\Gamma =G/H\), H being the kernel of the cyclotomic character. - 3. The Hodge-Tate decomposition, and a classification of representations of G over \(K={\mathbb{C}}\). - 4. A characterisation of the Lie algebra of the image of G under a p-adic representation. - 5. The Hodge-Tate, de Rham, and crystalline representations. - 6. A description of the Zariski closure of the image of G under the Hodge-Tate representation.
Reviewer: S.Vlăduţ

MSC:
14L05 Formal groups, \(p\)-divisible groups
11S20 Galois theory
14F30 \(p\)-adic cohomology, crystalline cohomology
22E50 Representations of Lie and linear algebraic groups over local fields