Abstract:Let $C$ be a smooth projective curve defined over $\Qbar$, let $\pi:\mathcal{E}\lra C$ be an elliptic surface and let $\sigma_{P_1},\sigma_{P_2},\sigma_{Q}$ be sections of $\pi$ (corresponding to points $P_1,P_2, Q$ of the generic fiber $E$ of $\mathcal{E}$). We obtain a precise characterization, expressed solely in terms of the dynamical relations between the points $P_1,P_2,Q$ with respect to the endomorphism ring of $E$, so that there exist infinitely many $ł\in C(\Qbar)$ with the property that for some nonzero integers $m_{1,ł},m_{2,ł}$, we have that $[m_{i,ł}](\sigma_{P_{i}}(ł))=\sigma_{Q}(ł)$ (for $i=1,2$) on the smooth fiber $E_ł$ of $\mathcal{E}$.
From: Negin Shadgar [view email]
[v1]
Wed, 11 Feb 2026 00:04:52 UTC (17 KB)
[v2]
Thu, 12 Feb 2026 02:33:56 UTC (17 KB)
[v3]
Fri, 29 May 2026 14:08:15 UTC (17 KB)
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