Local Fields

Focusing on local class field theory, this book explores the subject from a cohomological perspective, building on the methodologies of Hochschild and Artin-Tate. It delves into extensions of local fields, particularly abelian ones, and is structured into four parts. The initial sections cover foundational concepts of discrete valuation rings and Dedekind domains, followed by an examination of ramification phenomena. The text emphasizes the norm map within this framework, using additive and multiplicative polynomials for clarity, while maintaining accessibility for readers familiar with basic algebra and topology.