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Concept

Galois group

Related lectures (29)

Quotient by Galois Action

Explores quotient by Galois action, focusing on coatings, actions, and shares in various spaces.

Intermediate Coatings: Revisiting Galoisian Correspondence

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

Topology: Homomorphisms and Galois Theory

Explores homomorphisms in topology and delves into Galois theory.

Galois Correspondence

Covers the Galois correspondence, relating subgroups to intermediate fields.

Elliptic Curve Cryptography: Galois Fields

Explores Galois fields, elliptic curve cryptography, arithmetic operations, group structure, and practical examples in cryptography.

Galois Fields and Elliptic Curves

Introduces Galois fields, elliptic curves, factorization algorithms, and the discrete logarithm problem in cryptography.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Local structure of totally disconnected locally compact groups II

Explores the local structure of totally disconnected locally compact groups, covering commensurated subgroups, completions, local automorphisms, and the quasi-centre.

Galois Theory: Solvability and Radical Extensions Log in to Mediaspace to watch this video

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

Galois Theory: The Galois Correspondence Log in to Mediaspace to watch this video

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

Galois Theory Fundamentals Log in to Mediaspace to watch this video

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.

Dedekind Rings: Theory and Applications Log in to Mediaspace to watch this video

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

Galois Theory: Extensions and Residual Fields Log in to Mediaspace to watch this video

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

Norm Extension in Finite Fields Log in to Mediaspace to watch this video

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

Ramification and Structure of Finite Extensions Log in to Mediaspace to watch this video

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

Galois Theory: Recap and Transitivity Log in to Mediaspace to watch this video

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

Hensel's Lemma and Field Theory Log in to Mediaspace to watch this video

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

Galois Theory of Qp Log in to Mediaspace to watch this video

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

Purely Inseparable Decompositions Log in to Mediaspace to watch this video

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

Finite Extensions of Qp: Local Constancy Log in to Mediaspace to watch this video

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