Manin–Mumford conjecture for special subvarieties

Let $X$ be an algebraic variety over $\mathbb{C}$. Define a special subvariety of $X$ to be a translate by a torsion point of an abelian subvariety when $X$ is an abelian variety, or the product of torsion points with a subtorus when $X$ is a torus. A special point is a zero-dimensional special subvariety. Manin–Mumford conjecture. Every irreducible component of the Zariski closure of a set of special points is a special subvariety. This is presented as a general formulation of the classical Manin–Mumford conjecture; the supplied text gives no resolution status for this formulation.