Time: 15:10-17:35, Every Friday of Spring 2025 Semester
Venue: E10-320
Speaker: Ivan Fesenko, Paolo Dolce
Course Description:
Class field theory is the main achievement of algebraic number theory of the 20th century. The course starts with the study of various important properties of complete discrete valuations fields. Then it presents abstract class field theory, class field theory for local fields with finite residue field and class field theory for global fields. This presentation is believed to be the shortest and clearest among many expositions of class field theory. The course discusses proofs of all main results of class field theory for local fields with finite residue field, algebraic number fields and function fields of curves over finite fields. It also includes a presentation of Iwasawa–Tate’s theory of zeta integrals and its applications. The course also includes remarks on three generalisations of class field theory, active research areas of the 21st century: anabelian geometry, higher class field theory and Langlands correspondences.
