Hindry's integral torsion-point conjecture for abelian varieties

Let $k$) be a number field, let $S$ be a finite set of places of $k$ containing the archimedean places, and let ${\mathcal O}_{k,S}$ be the ring of $S$-integers. Let $A/k$ be an abelian variety, and let ${\mathcal A}_S/\operatorname{Spec}({\mathcal O}_{k,S})$ be a model of $A$. Let $D$ be an effective divisor on $A$, defined over $\overline{k}$, with at least one irreducible component that is not the translate of an abelian subvariety by a torsion point, and let $\overline{D}$ be its Zariski closure in ${\mathcal A}_S$. Define $A_{D,S}(\overline{\mathbb Z})_{\operatorname{tors}}$ to be the set of torsion points of $A(\overline{k})$ whose closure in ${\mathcal A}_S$ is disjoint from $\overline{D}$. Hindry's conjecture. The set $A_{D,S}(\overline{\mathbb Z})_{\operatorname{tors}}$ is not Zariski dense in $A$. This extends the Manin–Mumford phenomenon to torsion points satisfying an $S$-integrality condition; the paper presents it as a general conjecture for abelian varieties, with the elliptic-curve case supplied by the main theorem. Its general status is not resolved in the supplied text.