论文标题
在诺斯科特（Northcott）的财产和当地学位上
On the Northcott property and local degrees
论文作者
论文摘要
我们构建了$ \ mathbb {q} $的无限Galois Extensions $ k $ of Mathbb {q} $，它满足了诺斯科特（Northcott）的高度元素的属性，并且在$ k $中质量数的分裂行为可以从$ k $中的质量分裂行为推导。我们还举例说明了$ \ mathbb {q} $的Galois扩展名，它们在所有质数上都有有限的本地学位，并且不满足Northcott属性。
We construct infinite Galois extensions $K$ of $\mathbb{Q}$ that satisfy the Northcott property on elements of small height, and where this property can be deduced solely from the splitting behavior of prime numbers in $K$. We also give examples of Galois extensions of $\mathbb{Q}$ which have finite local degree at all prime numbers and do not satisfy the Northcott property.
