AI 中文总结
该研究推广了Gao-Ge-Kühne的间隙原理，通过阿代尔曲线与全局赋值域理论证明任意特征下阿贝尔簇子簇的一致高度间隙，还给出了Bogomolov猜想的新证明途径。
AI 中文摘要
我们证明了任意特征下阿贝尔簇的子簇的一致高度间隙，推广了Gao-Ge-Kühne提出的新间隙原理。我们的证明通过阿代尔曲线与全局赋值域理论完成，并证明了任意全局赋值域上的Bogomolov猜想。这提供了一种获得一致Bogomolov型结果的不同途径，与Dimitrov-Gao-Habegger-Kühne及Yuan的方法不同。首先，我们证明了全局赋值域上除子的Bogomolov猜想；随后通过归纳论证将一般子簇的情形归约为除子的情形。针对全局函数域的特殊情形，我们遵循Gubler与Yamaki的策略，得到了几何Bogomolov猜想的新证明。
英文摘要
We prove uniform height gaps for subvarieties of abelian varieties in arbitrary characteristic, extending the new gap principle of Gao-Ge-Kühne. Our proof goes through the theory of adelic curves and globally valued fields, and proves the Bogomolov conjecture for an arbitrary globally valued field. This gives a different way to obtain uniform Bogomolov-type results, differing from the approaches of Dimitrov-Gao-Habegger-Kühne and Yuan. First, we prove the Bogomolov conjecture over globally valued fields for divisors. We then reduce the case of general subvarieties to the case of divisors by an induction argument. Specializing to the case of global function fields, we obtain a new proof of the geometric Bogomolov conjecture following the strategy of Gubler and Yamaki.
Comments40 pages, comments welcome!
