  We perform an electronic structure study for cerium oxide homogeneously-doped
with cobalt impurities, focusing on the role played by oxygen vacancies and
structural relaxation. By means of full-potential ab-initio methods, we explore
the possibility of ferromagnetism as observed in recent experiments. Our
results indicate that oxygen vacancies seem to be crucial for the appearance of
a ferromagnetic alignment among Co impurities, obtaining an increasing tendency
towards ferromagnetism with growing vacancy concentration. The estimated
couplings cannot explain though, the experimentally observed room-temperature
ferromagnetism. In this systematic study, we draw relevant conclusions
regarding the location of the oxygen vacancies and the magnetic couplings
involved. In particular, we find that oxygen vacancies tend to nucleate in the
neighborhood of Co impurities and we get a remarkably strong ferromagnetic
coupling between Co atoms and the Ce^{3+} neighboring ions. The calculated
magnetic moments per cell depend on the degree of reduction which could explain
the wide spread in the magnetization values observed in the experiments.
