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Let k be a perfect field, and K be a totally ramified extension of K_0 = FracW(k) of degree e. To a semi-stable p-adic representation of G_K (the absoluteGalois group of K), one can classicaly associate two polygons : the Hodgepolygon et the Newton polygon. It is well known that the former lies below thelatter, and that they have same endpoints. In this note, we introduce a thirdpolygon gotten from the semi-simplification of the representation mod p, and,under some conditions on Hodge-Tate weights, we prove that it lies above theHodge polygon again with same endpoint. We finally examine one exempleassociated to a crystalline representation.

Polygones de Hodge, de Newton et de l'inertie mod\'er\'ee des repr\'esentations semi-stables