Jean-Pierre Serre Jean-Pierre Serre Marvin J. Greenberg
The goal of this book is to present local class field theory from the cohomo- logical 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 coho- mology....
The goal of this book is to present local class field theory from the cohomo- logical point of view, following the method inaugurated by Hochschild an...