An alumina exhibiting a structure with a porosity such that the volume of the pores having a diameter of between 70 and 2000 Å is between 0.15 and 0.50 ml/g, and comprising at least one alkali metal (M), such that the content by weight of alkali metal, expressed as M2O, is between 400 and 1500 ppm, with respect to the total weight of the alumina, and a process for the transformation of a feedstock comprising at least one alcohol into an olefinic effluent, said process comprising a stage of dehydration of said alcohol in the presence of the alumina according to the present invention, having an acidity and a structure with a porosity which are optimal.