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arXiv · 2611.03606

Isogeny rigidity under algebraic group actions and finite translation orbits

Paolo Dolce·Francesco Tropeano·Ekaterina Amerik
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Abstract

We study finite orbits generated by fibrewise translations on varieties carrying two abelian fibrations. Under natural dominance and generation hypotheses, non-isotriviality of the first family forces points with finite orbit to lie over proper closed subsets of both bases. This extends results of Corvaja, Tsimerman and Zannier to complex families of arbitrary, possibly different relative dimensions, including torsors. The proof combines relative Manin-Mumford with a general isogeny rigidity theorem for algebraic group actions.

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Paolo Dolce, Francesco Tropeano, Ekaterina Amerik. 2026-11-02. Isogeny rigidity under algebraic group actions and finite translation orbits. https://arxiv.org/abs/2611.03606

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