论文标题
不大的大田地
Big fields that are not large
论文作者
论文摘要
$ \ bar {\ mathbb {q}} $的子场$ k $是$ $ $，如果每个平滑的曲线$ c $ cub over $ k $都有理性点具有无限的许多理性点。 $ \ bar {\ mathbb {q}} $的子场$ k $是$ big $，如果每个正整数$ n $，$ k $，$ k $包含一个数字字段$ f $，则$ [f：\ mathbb {q}] $由$ n $划分。尽管我们找不到其起源，但所有大领域是否很大的问题似乎已经散发了一段时间。在本文中，我们表明有很多不大的领域。
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.
