  For a smooth, projective family of homogeneous varieties defined over a
number field, we show that if potential density holds for the rational points
of the base, then it also holds for the total space. A conjecture of Campana
and Peternell, known in dimension at most 4 and for certain higher dimensional
cases, would then imply potential density for the rational points of smooth
projective varieties over number fields whose tangent bundle is nef.

Algebraic Geometry;Number Theory