Hydroprocessing process of at least one gas oil cut having a weighted mean temperature between 240°C and 350°C, operating at a temperature between 250°C and 400°C, at a total pressure between 2 MPa and 10 MPa with a ratio of hydrogen volume to volume of hydrocarbon-containing feedstock between 100 and 800 litres per litre and at an Hourly Volume Rate which is defined by the ratio of the volume flow rate of liquid hydrocarbon-containing feedstock to volume of catalyst fed into the reactor between 1 and 10 h -1, using a catalyst comprising at least one metal of the group VIB and/or at least one metal of the group VIII of the periodic classification and a support comprising an amorphous mesoporous alumina, the hydroprocessing process comprising at least the following steps of preparation of said alumina: a) at least a first precipitation step a) of alumina, in an aqueous reaction medium, from at least one basic precursor selected from sodium aluminate, potassium aluminate, ammonia, sodium hydroxide and potassium hydroxide and at least one acid precursor selected from aluminium sulphate, aluminium chloride, aluminium nitrate, sulphuric acid, hydrochloric acid and nitric acid, wherein at least one of the basic or acid precursors comprises aluminium, the relative flow rate of the acid and basic precursors is selected so as to obtain a pH of the reaction medium between 8.5 and 10.5 and the flow rate of the acid and basic precursor(s) containing aluminium is adjusted so as to obtain a progress rate of the first step between 40 and 100%, the progress rate being defined as being the proportion of alumina formed as equivalent Al 2 O 3 during the precipitation step a) in relation to the total quantity of alumina formed at the end of the precipitation step(s), the step a) operating at a temperature between 10 and 50°C, and for a time between 2 minutes and 30 minutes, b) a thermal processing step of the suspension obtained at the end of the step a), at a temperature between 50 and 200°C for a time between 30 minutes and 5 hours allowing an alumina gel to be obtained, c) a filtering step of the suspension obtained at the end of the thermal processing step b), followed by at least one washing step of the gel obtained, d) a drying step of the alumina gel obtained at the end of the step c) in order to obtain a powder, e) a shaping step of the powder obtained at the end of the step d) in order to obtain the raw material, f) a thermal processing step of the raw material obtained at the end of the step e) at a temperature between 500 and 1000°C, with or without an air flow containing up to 60% by volume of water. a) at least a first precipitation step a) of alumina, in an aqueous reaction medium, from at least one basic precursor selected from sodium aluminate, potassium aluminate, ammonia, sodium hydroxide and potassium hydroxide and at least one acid precursor selected from aluminium sulphate, aluminium chloride, aluminium nitrate, sulphuric acid, hydrochloric acid and nitric acid, wherein at least one of the basic or acid precursors comprises aluminium, the relative flow rate of the acid and basic precursors is selected so as to obtain a pH of the reaction medium between 8.5 and 10.5 and the flow rate of the acid and basic precursor(s) containing aluminium is adjusted so as to obtain a progress rate of the first step between 40 and 100%, the progress rate being defined as being the proportion of alumina formed as equivalent Al 2 O 3 during the precipitation step a) in relation to the total quantity of alumina formed at the end of the precipitation step(s), the step a) operating at a temperature between 10 and 50°C, and for a time between 2 minutes and 30 minutes, b) a thermal processing step of the suspension obtained at the end of the step a), at a temperature between 50 and 200°C for a time between 30 minutes and 5 hours allowing an alumina gel to be obtained, c) a filtering step of the suspension obtained at the end of the thermal processing step b), followed by at least one washing step of the gel obtained, d) a drying step of the alumina gel obtained at the end of the step c) in order to obtain a powder, e) a shaping step of the powder obtained at the end of the step d) in order to obtain the raw material, f) a thermal processing step of the raw material obtained at the end of the step e) at a temperature between 500 and 1000°C, with or without an air flow containing up to 60% by volume of water.