Activator solid support for metallocenes as catalysts in the polymerization of olefins, characterized in that it consists of a group of support particles for a solid catalytic component, which are formed from at least one porous mineral oxide, the said particles having been modified in order to carry, on the surface, aluminum and/or magnesium Lewis-acid sites of formula: groups coming from a functionalization agent having reacted with —OH radicals carried by the base particles of the support, the functionalization reaction having been followed by a fluorination reaction. The catalytic system according to the invention comprises (a) a metallocene catalyst, which has, if required, been subjected to a prealkylation treatment; (b) a cocatalyst; and (c) an activator solid support for metallocene, as defined above, it being possible for the cocatalyst (b) to be absent if the metallocene catalyst (a) has been prealkylated.