Lectures related to Galois Theory of Qp

Covers the uniqueness of norm extension in finite fields and the construction of norms on finite extensions of Qp.

Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.

Galois Theory: The Galois Correspondence

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

Ramification and Structure of Finite Extensions

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

Galois Theory: Solvability and Radical Extensions

Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.

Decomposition & Inertia: Group Actions and Galois Theory

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

Galois Theory: Dedekind Rings

Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Galois Theory: Extensions and Residual Fields

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

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Galois Theory Fundamentals

Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.

Galois Theory: Recap and Transitivity

Covers the recap of Galois theory and emphasizes the transitivity of Galois groups.

Galois Correspondence

Covers the Galois correspondence, relating subgroups to intermediate fields.

Topology: Homomorphisms and Galois Theory

Explores homomorphisms in topology and delves into Galois theory.

Ramification Theory: Dedekind Recipe

Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.

Finite Degree Extensions

Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.

Purely Inseparable Decompositions

Explores purely inseparable decompositions, Galois property, and algebraic closures.

Dedekind Rings: Theory and Applications

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

Intermediate Coatings: Revisiting Galoisian Correspondence

Revisits the Galoisian correspondence and explores group actions in intermediate coatings.

Algebraic Extensions and Decomposition of Fok [x]

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

Algebraic Fields: Transcendence Degree

Explores transcendence degree in algebraic fields and classical analytic functions.