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Class field theory - Lecture 1

By Peter Stevenhagen

Appears in collection : Jean Morlet Chair - Spring School in Arithmetic Statistics / Chaire Jean Morlet - École de statistiques arithmétiques

This is the introductory lecture of the course on class field theory in the Research school on Arithmetic Statistics in May 2023. It briefly reviews the necessary algebraic number theory, and presents class field theory as the analogue of the Kronecker-Weber theorem over number fields. In a similar way, the Chebotarev density theorem is treated as an analogue of the Dirichlet theorem on primes in arithmetic progressions. Two further lectures dealt with idelic and cohomological reformulations of the main theorem of class field theory, and two more were devoted to power reciprocity laws and Redei reciprocity.

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