射影簇中支配椭圆曲线的非阿基米德整曲线
代数几何
2025-02-18 v3 数论
摘要
设 为特征为零的代数闭、完备非阿基米德赋值域。我们证明了非阿基米德 Green--Griffiths--Lang 猜想对不规则度为 1 的射影曲面成立。更确切地说，我们证明若 是一个无群（groupless）射影曲面且容许到一个椭圆曲线的支配态射，则 是 -解析 Brody 双曲的。我们证明中的主要成分是有关容许到椭圆曲线的支配态射的射影伪无群（pseudo-groupless）簇中非阿基米德整曲线的代数退化定理。
引用
@article{arxiv.2005.12353,
title = {Non-Archimedean entire curves in projective varieties dominating an elliptic curve},
author = {Jackson S. Morrow},
journal= {arXiv preprint arXiv:2005.12353},
year = {2025}
}
备注
The paper has been withdrawn by the author due to an error in the proof of Lemma 3.2. Section 1 up to Lemma 3.2 and Section 5 are to the best of the author's knowledge, still correct