An introduction to higher dimensional local fields and adeles

2012/04/03 by Matthew Morrow, Morrow, Matthew · 6 citations
Mathematics · #11F85 (Primary) 19F05 #14B99 (Secondary) #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1204.0586

openalex publication_date 2012/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Representations of Higher Adelic Groups and Arithmetic

Cited by

• Selective Integration on Higher Adeles and the Euler Characteristic of Surfaces
• Embeddings and intersections of adelic groups
• Automorphicity and Mean-Periodicity
• Localizations of Morava E-theory and deformations of formal groups
• Zeta Functions on Arithmetic Surfaces
• Higher adeles and non-abelian Riemann-Roch

Related

• Invitation to higher local fields, Part I, section 1: Higher dimensional local fields
• Invitation to higher local fields, Part I, section 10: Explicit higher local class field theory
• Two-Dimensional Local-Global Class Field Theory in Positive Characteristic
• Invitation to higher local fields, Part II, section 8: Higher local skew fields
• Invitation to higher local fields, Part I, section 16: Higher class field theory without using K-groups