martensitic stainless steel, method of manufacturing a semi-finished product in this steel cutting tool made from this semi-finished product A martensitic stainless steel. This steel is principally intended for the manufacture of cutting tools, in particular of cutlery, such as scalpels, scissors blades, or knife blades or blades of household robots. The steels used in the cutlery must have a corrosion resistance, polishability and a high hardness. Martensitic stainless steels currently used to make the blades of the cutting tools, such as steels of types 1 .4021, .4028 IN 1 and IN-1 .4034, has contents of Cr less than or equal to 14 or to 14, 5% by weight and C in varying amounts, or 0.16% -0.25% for the iN 1 .4021, 0.26 to 0.35% for the iN 1 .4028 and .43 to .50 iN 1% for .4034. The hardness of the steel level depends primarily on the content of C. When even better resistance to corrosion is desired, the nuance EN 1 .4419 to 0.36 to 0.42% C, 13.0 to 14.5% Cr and 0.60 to 1, 00% of MB can be used. During their manufacture, these steels are typically prepared in an AOD or VOD converter, then continuously cast as slabs, blooms or billets, and then hot-rolled to give a coil, a rolled bar or wire rod. They are then subjected to annealing to obtain a ferritic structure containing carbides, which is sufficiently soft to allow to perform cold rolling to flat products, or to facilitate the sawing before forging of the hot-rolled semi-finished product for long products. The product then undergoes recrystallization annealing. In this softened state of recrystallized ferrite containing carbides, the product is cut to give it its final shape, for example that of a knife blade, before undergoing heat treatment comprising a high austenitizing temperature, typically between 950 ° C and 1150 ° C, followed by quenching to room temperature which leads to a mainly martensitic structure. In this martensitic state the product has a high hardness, even higher than the carbon content is important, but it also has great fragility. Annealing treatment, typically between 100 ° C and 300 ° C, is then carried out to reduce the brittleness without too lower hardness. The blade is then subjected to various operations including sharpening and polishing to give it its cut quality and its aesthetic appearance. None of the four cited nuances allows both good corrosion resistance, a good surface finish and high hardness, for a reasonable cost. The nuance EN 1 .4419 to good corrosion resistance and high hardness, but it is prohibitively expensive due to the addition of Mo in large quantities. The nuance EN 1 .4034 has a high hardness, but also a poor surface appearance after polishing, because of the large presence of undissolved carbides during austenitizing, due to the high content of C of this shade . The corrosion resistance is insufficient because the Cr content is not high enough in the matrix, especially as a part of Cr is trapped in undissolved carbides. Moreover, it happens regularly that the blade edge is the seat of a crevice corrosion, from the decohesion large primary carbides appear at the end of solidification in continuous casting. The nuances less charged C EN 1 .4021 and .4028 1 have lower hardness, without having a place in sufficient corrosion due to Cr contents too low. The present invention aims to solve the problems mentioned above. It aims in particular to provide a martensitic stainless steel tool for cutting as economically as possible, which, however, has both good corrosion resistance, a good polishing and high hardness. To this end the invention relates to a martensitic stainless steel, characterized in that its composition is, in percentages by weight: - 0.10%