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We extend Dill's generalized Vojta-Rémond inequality to proper adelic curves of characteristic zero, under an explicit Siegel hypothesis. The geometric case is closely related to recent work on Mordell-Lang plus geometric Bogomolov for semi-abelian varieties. Our formulation retains Dill's generality for products of distinct projective varieties. The appendix establishes the Siegel input for arithmetic function fields with nef and big polarizations on the model.
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Ningjun Jiang (2026) studied this question.
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