PAPER / ARXIV:2609.13735

Finiteness of an Isogeny Class via Equidistribution

Jit Wu Yap

RESUMO

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.

NO MESMO MAPA

Papers relacionados

math.NT18 de set. de 2026

Asymptotic counting of integers with prime factors $p_{r^a s^b}$

Mehdi Golafshan

Finiteness of an Isogeny Class via Equidistribution

Papers relacionados

Asymptotic counting of integers with prime factors $p_{r^a s^b}$

A uniform proof approach for congruences modulo 3 for partitions with $k$-colored odd parts

Sumsets of Ahlfors--David regular sets

On the Hiraga-Ichino-Ikeda conjecture on formal degrees for $\mathrm{G}_2$

Endoscopic description of the local Langlands correspondence for $\mathrm{G}_2$

A new family of maximal curves not covered by the Hermitian curve