Class field theory, its three main generalisations, and applications
type: Item
instance of: scholarly article
title: Class field theory, its three main generalisations, and applications
zbMATH Open document ID: 1482.11152
DOI: 10.4171/EMSS/45
published in: EMS Surveys in Mathematical Sciences
publication date: 2021-09-13T00:00:00Z
review text: In this paper, the author presents branches of class field theory. He gives us special and general approaches to class field theory, and discusses their roles. In particular, the three main generalisations of class field theory: Higher-class field theory, Langlands correspondences and anabelian geometry, and their further developments are discussed. He suggests several directions of unification of the generalisations of class field theory.
reviewed by: Abdelmalek Azizi
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11S37
Mathematics Subject Classification ID: 12-03
Mathematics Subject Classification ID: 19F05
zbMATH DE Number: 7394434
zbMATH Keywords: class field theory
zbMATH Keywords: general class field theory
zbMATH Keywords: special class field theory
zbMATH Keywords: higher class field theory
zbMATH Keywords: Langlands correspondences
zbMATH Keywords: anabelian geometry
zbMATH Keywords: elliptic curves over global fields
zbMATH Keywords: zeta integrals
zbMATH Keywords: higher adelic geometry and analysis
zbMATH Keywords: IUT theory
author: I. B. Fesenko
MaRDI profile type: Publication
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