  Let $A \rightarrow S$ be an abelian scheme over a $p$-adic field, and let $s
\colon S \rightarrow A$ be a section. We study the torsion locus $\bigcup
\limits_{n \geq 1} s^{-1}(A[n])$ on $S$, and we show that torsion points on $S$
of different orders stay away from each other.
