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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.
 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