  We formulate a conjecture for semiabelian varieties A over number fields that
includes both the Mordell-Lang conjecture (now proven) and the Bogomolov
conjecture. We prove the "Mordellic" (finitely generated) part of the
conjecture when A is isogenous to the product of an abelian variety and a
torus. The proof makes use of the Mordell-Lang conjecture, the Bogomolov
conjecture, and an equidistribution theorem.
