Class field theory, its three main generalisations, and applications
Ivan FesenkoUniversity of Nottingham, UK
This work presents branches of class field theory. Special and general approaches to class field theory, and their roles, are discussed. Three main generalisations of class field theory: higher class field theory, Langlands correspondences and anabelian geometry, and their further developments are discussed. Several directions of unification of generalisations of class field theory are proposed. New fundamental open problems are included.
Cite this article
Ivan Fesenko, Class field theory, its three main generalisations, and applications. EMS Surv. Math. Sci. 8 (2021), no. 1/2, pp. 107–133DOI 10.4171/EMSS/45