论文标题
Zariski空间的孤立点
Isolated points of the Zariski space
论文作者
论文摘要
令$ d $是一个积分域，$ l $是包含$ d $的字段。我们研究Zariski空间的隔离点$ \ MATHRM {ZAR}（L | D）$，相对于可构造拓扑。特别是，我们完全表征了$ l $（作为一个点）隔离时，并且在假设$ l $是$ d $的商字段的情况下，隔离尺寸$ 1 $的估值域；结果，当$ d $是noetherian域时，我们发现$ \ mathrm {zar}（d）$的所有隔离点。我们还表明，如果$ v $是一个估值域，而$ l $超过$ v $，则$ v $至$ l $的扩展名没有孤立的积分。
Let $D$ be an integral domain and $L$ be a field containing $D$. We study the isolated points of the Zariski space $\mathrm{Zar}(L|D)$, with respect to the constructible topology. In particular, we completely characterize when $L$ (as a point) is isolated and, under the hypothesis that $L$ is the quotient field of $D$, when a valuation domain of dimension $1$ is isolated; as a consequence, we find all isolated points of $\mathrm{Zar}(D)$ when $D$ is a Noetherian domain. We also show that if $V$ is a valuation domain and $L$ is transcendental over $V$ then the set of extensions of $V$ to $L$ has no isolated points.
