Lectures related to Galois Correspondence

Galois Theory: Extensions and Residual Fields

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

Galois Theory: The Galois Correspondence

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

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 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.

Topology: Homomorphisms and Galois Theory

Explores homomorphisms in topology and delves into Galois theory.

Ramification and Structure of Finite Extensions

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

Galois Theory of Qp

Explores the Galois theory of Qp, covering algebraic extensions, inertia groups, and cyclic properties.

Finite Degree Extensions

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

Galois Theory: Solvability and Radical Extensions

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

Galois Theory: Recap and Transitivity

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

Dimension Theory of Rings

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Norm Extension in Finite Fields

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

Algebras and Field Extensions

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

Galois Theory: Dedekind Rings

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

Hensel's Lemma and Field Theory

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

Purely Inseparable Decompositions

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

Linear Lie Groups: Definitions and Theorems

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Ramification Theory: Residual Fields and Discriminant Ideal

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.