The canonical height of a section of an elliptic scheme over a curve equals the integral of the Betti form over the base, and this measure coincides with the dynamical equidistribution measure.
On the $p$-adic distribution of torsion values for a section of an abelian scheme
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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.
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On the torsion values for sections of an elliptic scheme
The canonical height of a section of an elliptic scheme over a curve equals the integral of the Betti form over the base, and this measure coincides with the dynamical equidistribution measure.