An introduction to higher dimensional local fields and adeles

TL;DR

This paper introduces higher dimensional local fields and adeles, covering foundational theory, topologies, and class field theory, providing a comprehensive overview for researchers in algebraic number theory.

Contribution

It offers an accessible introduction to higher dimensional local fields and adeles, including recent developments in their topologies and class field theory.

Findings

Summarizes the foundational aspects of higher dimensional local fields.

Details the topologies on higher dimensional local fields.

Provides an overview of higher dimensional local class field theory.

Abstract

These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local class field theory.