A composition - based on Al and Ce in the form of oxides (composition C1); or - based on Al, Ce and La in the form of oxides (composition C2), with the following proportions: - the proportion of CeO 2 is between 3.0 wt% and 35.0 wt%; - the proportion of La 2 O 3 (for composition C2 only) is between 0.1 wt% and 6.0 wt%; - the remainder as Al 2 O 3; exhibiting the following porosity profile: - a pore volume in the range of pores with a size of between 5 nm and 100 nm which is between 0.35 and 1.00 mL/g; and - a pore volume in the range of pores with a size of between 100 nm and 1000 nm which is less than or equal to 0.15 mL/g, these pore volumes being determined by means of the mercury porosimetry technique; and the following properties: - a mean size of the crystallites after calcination in air at 1100°C for 5 hours (denoted D 1100°C-5h) which is lower than 45.0 nm, preferably lower than 40.0 nm; - a mean size of the crystallites after calcination in air at 900°C for 2 hours (denoted D 900°C-2h) which is lower than 25.0 nm, preferably lower than 20.0 nm, even more preferably lower than 15.0 nm; and - an increase ΔD of the mean size of the crystallites lower than 30.0 nm, preferably lower than 25.0 nm, ΔD being calculated with the following formula: ΔD = D 1100°C-5h - D 900°C-2h; the mean size of the crystallites being being obtained by XRD from the diffraction peak of the cubic phase corresponding to cerium oxide, generally present at 2θ between 28.0° and 30.0°. - based on Al and Ce in the form of oxides (composition C1); or - based on Al, Ce and La in the form of oxides (composition C2), with the following proportions: - the proportion of CeO 2 is between 3.0 wt% and 35.0 wt%; - the proportion of La 2 O 3 (for composition C2 only) is between 0.1 wt% and 6.0 wt%; - the remainder as Al 2 O 3; - the proportion of CeO 2 is between 3.0 wt% and 35.0 wt%; - the proportion of La 2 O 3 (for composition C2 only) is between 0.1 wt% and 6.0 wt%; - the remainder as Al 2 O 3; exhibiting the following porosity profile: - a pore volume in the range of pores with a size of between 5 nm and 100 nm which is between 0.35 and 1.00 mL/g; and - a pore volume in the range of pores with a size of between 100 nm and 1000 nm which is less than or equal to 0.15 mL/g, - a pore volume in the range of pores with a size of between 5 nm and 100 nm which is between 0.35 and 1.00 mL/g; and - a pore volume in the range of pores with a size of between 100 nm and 1000 nm which is less than or equal to 0.15 mL/g, these pore volumes being determined by means of the mercury porosimetry technique; and the following properties: - a mean size of the crystallites after calcination in air at 1100°C for 5 hours (denoted D 1100°C-5h) which is lower than 45.0 nm, preferably lower than 40.0 nm; - a mean size of the crystallites after calcination in air at 900°C for 2 hours (denoted D 900°C-2h) which is lower than 25.0 nm, preferably lower than 20.0 nm, even more preferably lower than 15.0 nm; and - an increase ΔD of the mean size of the crystallites lower than 30.0 nm, preferably lower than 25.0 nm, ΔD being calculated with the following formula: ΔD = D 1100°C-5h - D 900°C-2h; the mean size of the crystallites being being obtained by XRD from the diffraction peak of the cubic phase corresponding to cerium oxide, generally present at 2θ between 28.0° and 30.0°. - a mean size of the crystallites after calcination in air at 1100°C for 5 hours (denoted D 1100°C-5h) which is lower than 45.0 nm, preferably lower than 40.0 nm; - a mean size of the crystallites after calcination in air at 900°C for 2 hours (denoted D 900°C-2h) which is lower than 25.0 nm, preferably lower than 20.0 nm, even more preferably lower than 15.0 nm; and - an increase ΔD of the mean size of the crystallites lower than 30.0 nm, preferably lower than 25.0 nm, ΔD being calculated with the following formula: ΔD = D 1100°C-5h - D 900°C-2h;