有限几何中的域约化与线性集
Field reduction and linear sets in finite geometry
摘要：
基于有限域中子域的简单和易于理解的概念，称为“域归约”的技术已证明是有限几何中非常有用和强大的工具。在本文中，我们详细介绍了这种技术。领域减少投影和极空间的形式化和Deskiesian传播和线性集的联系进行了详细解释。本文研究了线性集和离散空间的最新结果和一些基本问题。域约简的相关性通过讨论阻塞集和半域的应用来说明。
英文摘要：
Based on the simple and well understood concept of subfields in a finite field, the technique called `field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field reduction for projective and polar spaces is formalized and the links with Desarguesian spreads and linear sets are explained in detail. Recent results and some fundamental ques- tions about linear sets and scattered spaces are studied. The relevance of field reduction is illustrated by discussing applications to blocking sets and semifields.
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