通过等分布证明同源类的有限性
Finiteness of an Isogeny Class via Equidistribution
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中文总结 AI 辅助
本文利用等分布思想，将数域上同源类有限性的证明归约到有限域情形，从而给出沙法列维奇猜想的新证明。
中文摘要 AI 辅助
在最近一篇非常优美的论文中，谢俊义和杨子全通过将法尔廷斯同源定理归约到有限域上的泰特定理，给出了其在数域上的一个新证明。我们表明，同样的思想可以被调整，用以从有限域上同源类的有限性出发，证明数域上同源类的有限性。因此，我们获得了数域上沙法列维奇猜想的一个新证明。本文的证明是通过使用GPT6 Astra Ultra获得的。
英文摘要
In a very recent, beautiful paper, Junyi Xie and Ziquan Yang gave a new proof of Faltings' isogeny theorem over number fields by reducing to Tate's theorem over finite fields. We show that the same ideas can be adapted to prove finiteness of an isogeny class over number fields from the finiteness of an isogeny class over finite fields. Hence we obtain a new proof of the Shafarevich conjecture over number fields. The proof in this paper was obtained through the use of GPT6 Astra Ultra.
