In mathematics, local class field theory, introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field ...

11 дек. 2017 г. · The goal of local class field theory is to classify all finite abelian extensions of a given local field K. Rather than considering each finite ...

The local reciprocity law is an analogue of the Artin reprocity law for number fields. We also get an analogue of the existence of ray class fields.

8 дек. 2015 г. · The goal of local class field theory is to classify all finite abelian extensions of a given local field K. Rather than considering each finite ...

Class field theory describes the abelian extensions of a local or global field in terms of the arithmetic of the field itself. These notes contain an ...

There are essentially two main theorems of local class field theory: the Reciprocity theorem and the Existence theorem. To explain the Reciprocity theorem, we ...

and therefore what class field theory deals with is the abelian extensions of K. There are two types of fields K we use in class field theory: local fields, Qp.

We prove local class field theory via Lubin-Tate theory and the Hasse- Arf theorem. The only prerequisites are Galois theory (including cyclotomic extensions, ...

\Bibitem{Par84} \by A.~N.~Parshin \paper Local class field theory \inbook Algebraic geometry and its applications \bookinfo Collection of articles

We will spend the entirety of Chapter 4 establishing local class field theory , a classification of the abelian extensions of a local field.