Ramification Theory: Residual Fields and Discriminant Ideal

Related lectures (32)

Page 3 of 4

Explores the definition of Q_p and the completion of Q,1(p) to form Qp.

Covers the Galois correspondence, relating subgroups to intermediate fields.

Introduces algebras over a field, k-linear endomorphisms, and commutative algebras.

Explores the Galois correspondence and solvability by radicals in polynomial equations.

Covers matrix calculations, basis change, field extensions, complex numbers modulus, and polar decomposition.

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

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

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

Explores homomorphisms in topology and delves into Galois theory.