局部域

《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 completing an algebraic number field; that is one of the aspects of "localisation".

The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group cohomology. Local class field theory, strictly speaking, does not appear until the fourth part.