发表机构
Beijing International Center for Mathematical Research, Peking University; Department of Mathematics & Institute of Mathematical Sciences, Chinese University of Hong Kong（北京大学北京国际数学研究中心; 香港中文大学数学系及数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
利用 Yuan 的非阿基米德等分布定理，将同态和半单性从有限域提升到数域，从而直接由 Tate 定理推出 Faltings 同源定理的新证明。
AI 中文摘要
我们给出了 Faltings 同源定理的一个新证明。更精确地说，我们证明了 Yuan 的非阿基米德等分布定理可用于将同态和半单性从有限域“提升”到数域，从而将 Faltings 定理直接归结为 Tate 定理。
英文摘要
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.
Comments13 pages, 1 figure
