A method for producing a cerium oxide, characterized as comprising heating a cerium salt at a high speed up to a burning temperature, followed by burning; a cerium oxide abrasive comprising a cerium oxide produced by the method and pure water; an abrasive containing a slurry comprising a medium and, dispersed therein, cerium oxide particles having, in a powder X-ray diffraction chart, an intensity ratio of the area of a primary peak appearing at 27 to 30° to that of a secondary peak appearing at 32 to 35° (primary peak/secondary peak) of 3.20 or more; an abrasive containing a slurry comprising a medium and, dispersed therein, cerium oxide particles having a bulk density of 6.5 g/cm3 or less; an abrasive containing a slurry comprising a medium and, dispersed therein, abrasive grains having pores; a method for polishing a substrate, characterized as comprising polishing a specific substrate using the above abrasive; and a method for manufacturing a semiconductor device, characterized as comprising a step of polishing with the above abrasive.