Topology: Homomorphisms and Galois Theory

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Galois Theory: Extensions and Residual Fields

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

Galois Theory: Recap and Transitivity

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

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.

Automorphism Groups: Trees and Graphs III

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

Topology: Lecture Notes 2021

Covers polygonal performance, homomorphisms, and the Klein bottle in topology.

Galois Theory: The Galois Correspondence

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

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 Correspondence

Covers the Galois correspondence, relating subgroups to intermediate fields.

Dimension Theory of Rings

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