An intervertebral disc prosthesis comprising at least three pieces that include a first plate (1), a second plate (2) and a mobile core (3) at least with respect to one of the plates (1, 2), having the core (3) a curved surface in contact with at least a part of a complementary curved surface of the first plate (1) 5 and a substantially flat surface in contact with at least a part of a substantially flat surface of the second plate (2 ), characterized in that the core (3) comprises, on said substantially flat surface in contact with the substantially flat surface of the second plate (2): - a plurality of concave alveoli, arranged to facilitate the sliding of the core (3) with respect to to this substantially flat surface of the second plate (2), or - at least one prolonged blind hole (41), to the periphery of this substantially flat surface, by means of grooves (410) forming channels by means of The interstitial fluid of the surrounding tissue can play a lubricating role to improve the sliding of the core (3) on the substantially flat surface of the second plate (2), when the prosthesis is placed in the patient.Una prótesis de disco intervertebral que comprende al menos tres piezas que incluyen una primera placa (1), una segunda placa (2) y un núcleo (3) móvil al menos con respecto a una de las placas (1, 2), teniendo el núcleo (3) una superficie curvada en contacto con al menos una parte de una superficie curvada complementaria de la primera placa (1) 5 y una superficie sustancialmente plana en contacto con al menos una parte de una superficie sustancialmente plana de la segunda placa (2), caracterizada porque el núcleo (3) comprende, sobre dicha superficie sustancialmente plana en contacto con la superficie sustancialmente plana de la segunda placa (2): - una pluralidad de alvéolos cóncavos, dispuestos para facilitar el deslizamiento del núcleo (3) con respecto a esta superficie sustancialmente plana de la segunda placa (2), o - al menos un agujero (41) ciego prol
