Lectures related to Hilbert class field

Explores ramified extensions and Eisenstein polynomials, showcasing their applications in mathematical contexts.

Discusses the classification of finite extensions of Qp and introduces Krassner's Lemma on root continuity.

Explores the Localization Theorem in Dedekind rings, isomorphism induced by injection, and ramification in field theory.

Explores decomposition groups, inertia subgroups, Galois theory, unramified primes, and cyclotomic fields in group actions and field extensions.

Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.