Year: 2026
Type: preprint
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. In the appendix joint with Yap, we explain how an ultraproduct variant of our method gives another proof of the Shafarevich conjecture, and hence a new route to the Mordell conjecture via Parshin's trick.
Source: arXiv (Cornell University)
Authors: Xie, Junyi, Yang, Ziquan
Institution: Peking University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212172827