局部域

在数学上，局部域是一类特别的域，它有非平凡的绝对值，此绝对值赋予的拓扑是局部紧的。局部域可粗分为两类:一种的绝对值满足阿基米德性质(称作阿基米德局部域)，另一种的绝对值不满足阿基米德性质(称作非阿基米德局部域)。在数论中，数域的完备化给出局部域的典型例子。内容介绍《局部域》主要内容:The goal of this book is to present local class field theory from the cohomological point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions--primarily abelian--of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by