Galois Theory: Extensions and Residual Fields

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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.

Ramification and Structure of Finite Extensions

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

Galois Theory: The Galois Correspondence

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

Finite Degree Extensions

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

Topology: Homomorphisms and Galois Theory

Explores homomorphisms in topology and delves into Galois theory.

Norm Extension in Finite Fields

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

Galois Theory: Solvability and Radical Extensions

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

Galois Correspondence

Covers the Galois correspondence, relating subgroups to intermediate fields.

Galois Theory: Recap and Transitivity

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