论文标题
étale-open拓扑结构和稳定的田野猜想
The étale-open topology and the stable fields conjecture
论文作者
论文摘要
对于任意字段$ k $和$ k $ -variety $ v $，我们在$ k $ - $ v $的集合$ v（k）$ of $ v $上引入了étale-open拓扑。当$ k $分别封闭，真实关闭或$ p $ airply封闭时，这种拓扑与Zariski拓扑，欧几里得拓扑或估值拓扑相符。典型开放拓扑的拓扑特性对应于$ k $的代数属性。例如，$ \ mathbb {a}^1（k）$上的open-open拓扑不是离散的，并且仅当$ k $很大。作为一个应用程序，我们表明一个大稳定场是明显关闭的。
For an arbitrary field $K$ and $K$-variety $V$, we introduce the étale-open topology on the set $V(K)$ of $K$-points of $V$. This topology agrees with the Zariski topology, Euclidean topology, or valuation topology when $K$ is separably closed, real closed, or $p$-adically closed, respectively. Topological properties of the étale-open topology corresponds to algebraic properties of $K$. For example, the étale-open topology on $\mathbb{A}^1(K)$ is not discrete if and only if $K$ is large. As an application, we show that a large stable field is separably closed.
