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Related lectures (32)

Galois Theory: The Galois Correspondence

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

Galois Theory: Solvability and Radical Extensions

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

Galois Theory: Dedekind Rings

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

Galois Theory of Qp

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

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.

Intermediate Coatings: Revisiting Galoisian Correspondence

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

Dedekind Rings: Theory and Applications

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

Galois Theory: Extensions and Residual Fields

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

Quotient by Galois Action

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

Ramification and Structure of Finite Extensions

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

Norm Extension in Finite Fields

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

Polynomials: Theory and Operations

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

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.

Galois Theory: Recap and Transitivity

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

Ramification Theory: Dedekind Recipe

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

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.

Bar Construction: Homology Groups and Classifying Space

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

Galois Fields and Elliptic Curves

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

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