Decomposition & Inertia: Group Actions and Galois Theory

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Related lectures (32)

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.

Intermediate Coatings: Revisiting Galoisian Correspondence

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

Elliptic Curve Cryptography: Galois Fields

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

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.

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.

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 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.

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 of Qp Log in to Mediaspace to watch this video

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

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.

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.

Dimension Theory of Rings Log in to Mediaspace to watch this video

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

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.

Ramification Theory: Residual Fields and Discriminant Ideal Log in to Mediaspace to watch this video

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

Finite Degree Extensions Log in to Mediaspace to watch this video

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

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.

Ramification Theory: Dedekind Recipe Log in to Mediaspace to watch this video

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

Galois Theory: Dedekind Rings Log in to Mediaspace to watch this video

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

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