任意特征中代数函数域的位置
Places of algebraic function fields in arbitrary characteristic
摘要：
本文考虑任意特征的代数函数域$F|K$的所有位置的Zerkiki空间，并利用其分片拓扑研究其结构.我们表明，某些具有良好属性的地方（例如，素除子，最大秩的地方，零维离散的地方）在这个拓扑中是稠密的。进一步，我们给出了在F意义下的大场的几个等价刻画。Pop的Annals论文{ \it Embedding problems over large fields}。我们还研究了当$L$存在$K$ -有理空间时，域$K$在扩域$L$中是否存在闭的问题.在附录中，我们证明了具有Zebraki拓扑的Zebraki空间是拟紧的，并且它是谱空间。
英文摘要：
We consider the Zariski space of all places of an algebraic function field $F|K$ of arbitrary characteristic and investigate its structure by means of its patch topology. We show that certain sets of places with nice properties (e.g., prime divisors, places of maximal rank, zero-dimensional discrete places) lie dense in this topology. Further, we give several equivalent characterizations of fields that are large, in the sense of F. Pop's Annals paper {\it Embedding problems over large fields}. We also study the question whether a field $K$ is existentially closed in an extension field $L$ if $L$ admits a $K$-rational place. In the appendix, we prove the fact that the Zariski space with the Zariski topology is quasi-compact and that it is a spectral space.
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