Reports optimal estimates on height variation in isogeny classes of abelian varieties, suggesting deeper insights into their structure.
We give optimal estimates on the variation of the differential and modular heights within an isogeny class of abelian varieties defined over the function field of a curve (in any characteristic). We also prove a parallelogram inequality for abelian varieties in this context, and deduce corollaries of these results.
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Griffon et al. (2026) studied this question.
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