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Ramification and Structure of Finite Extensions
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Related lectures (34)
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Explores homomorphisms in topology and delves into Galois theory.
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Galois Theory: The Galois Correspondence
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Decomposition & Inertia: Group Actions and Galois Theory
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Galois Theory: Extensions and Residual Fields
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Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.
Dedekind Rings: Theory and Applications
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Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.
Dedekind Rings: Factorisation and Ideal Class Group
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Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.
Galois Theory Fundamentals
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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: Recap and Transitivity
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Covers the recap of Galois theory and emphasizes the transitivity of Galois groups.
Ramification Theory: Residual Fields and Discriminant Ideal
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Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.
Galois Theory of Qp
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Purely Inseparable Decompositions
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Explores purely inseparable decompositions, Galois property, and algebraic closures.
Finite Extensions of Qp: Local Constancy
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Dedekind Rings: Integral Extensions and Noetherian Rings
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Properties of Euclidean Domains
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Finite Degree Extensions
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Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.
Norm Extension in Finite Fields
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Covers the uniqueness of norm extension in finite fields and the construction of norms on finite extensions of Qp.
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