Faltings' Isogeny Theorem via Equidistribution

Junyi Xie; Ziquan Yang

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arXiv · 2609.10302

Faltings' Isogeny Theorem via Equidistribution

Junyi Xie·Ziquan Yang

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Abstract

We give a new proof of Faltings' isogeny theorem. More precisely, we show that Yuan's non-archimedean equidistribution theorem can be used to "pump" homomorphisms and semisimplicity from finite fields to number fields, thereby reducing Faltings' theorem directly to Tate's theorem.

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Junyi Xie, Ziquan Yang. 2026-09-09. Faltings' Isogeny Theorem via Equidistribution. https://arxiv.org/abs/2609.10302

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