面积不大的大油田
Big fields that are not large
摘要：
$\bar{\mathbb{Q}}$的子域$K$是$large$，如果$K$上的每个具有有理点的光滑曲线$C$具有无穷多个有理点。如果对于每个正整数$n$，$K$包含数字字段$F$，其中$[F:\mathbb{Q}]$可被$n$整除，则$\bar{\mathbb{Q}}$的子字段$K$是$big$。是否所有的大场都是大的这个问题似乎已经流传了一段时间，尽管我们一直无法找到它的起源。在本文中，我们表明，有大的领域是不大的。
英文摘要：
A subfield $K$ of $\bar{\mathbb{Q}}$ is $large$ if every smooth curve $C$ over $K$ with a rational point has infinitely many rational points. A subfield $K$ of $\bar{\mathbb{Q}}$ is $big$ if for every positive integer $n$, $K$ contains a number field $F$ with $[F:\mathbb{Q}]$ divisible by $n$. The question of whether all big fields are large seems to have circulated for some time, although we have been unable to find its origin. In this paper we show that there are big fields that are not large.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
