The present invention relates to high molecular weight homopolymers and copolymers of ethene, which homopolymer or copolymer is obtained by polymerizing the monomer(s) at a temperature of from 70.degree. to 150.degree. C. and under a pressure of from 2 to 150 bar in contact witha chromium trioxide catalyst, (1) loading a support based on silicon dioxide with (2) either chromium trioxide or a chromium compound capable of being converted to chromium trioxide under the conditions of stage (3) below and then (3) heating the resulting intermediate in a gas stream containing oxygen, the support (1) being a special silica xerogel obtained by extracting not more than 30% of the water from a silica hydrogel by means of an alkanol, an alkanone or a mixture thereof followed by drying, comminution and fractional screening.