Class field theory, its three main generalisations, and applications

Fesenko, Ivan

Abstract

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.

Citation

Fesenko, I. (2021). Class field theory, its three main generalisations, and applications. EMS Surveys in Mathematical Sciences, 8(1-2), 107-133. https://doi.org/10.4171/emss/45

• Journal Article Type: Article
• Acceptance Date: May 28, 2021
• Online Publication Date: Aug 31, 2021
• Publication Date: Sep 1, 2021
• Deposit Date: Jun 2, 2021
• Publicly Available Date: Jun 2, 2021
• Journal: EMS Surveys in Mathematical Sciences
• Print ISSN: 2308-2151
• Electronic ISSN: 2308-216X
• Publisher: European Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 8
• Issue: 1-2
• Pages: 107-133
• DOI: https://doi.org/10.4171/emss/45
• Keywords: General Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/5621996
• Publisher URL: https://www.ems-ph.org/journals/show_abstract.php?issn=2308-2151&vol=8&iss=1&rank=5
• Additional Information: https://ems.press/journals/emss "Issues of this journal published between 1 January 2021 and 31 December 2021 are accessible as open access under our Subscribe to Open model."