Geodesic
Class field theory, its three main generalisations, and applications
Ivan Fesenko1
1University of Nottingham, UK
EMS surveys in mathematical sciences, Tome 8 (2021), pp. 107-133

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DOI

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.
DOI : 10.4171/emss/45
Classification : 11-XX, 12-XX, 19-XX
Mots-clés : Class field theory, general class field theory, special class field theory, higher class field theory, Langlands correspondences, anabelian geometry, elliptic curves over global fields, zeta integrals, higher adelic geometry and analysis, IUT theory

Ivan Fesenko  1

1 University of Nottingham, UK 
Ivan Fesenko. Class field theory, its three main generalisations, and applications. EMS surveys in mathematical sciences, Tome 8 (2021), pp. 107-133. doi: 10.4171/emss/45
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     doi = {10.4171/emss/45},
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