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Variation of height in an isogeny class over a function field

  • Richard Griffon

    Université Clermont Auvergne, Aubière, France

  • Samuel Le Fourn

    Université Grenoble Alpes, Gières, France

  • Fabien Pazuki

    University of Copenhagen, Denmark
Variation of height in an isogeny class over a function field cover
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Abstract

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.

Cite this article

Richard Griffon, Samuel Le Fourn, Fabien Pazuki, Variation of height in an isogeny class over a function field. Doc. Math. (2026), published online first

DOI 10.4171/DM/1094