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Ramification Theory: Dedekind Recipe
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Related lectures (32)
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Galois Theory: Dedekind Rings
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Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.
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: Solvability and Radical Extensions
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Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.
Dedekind Rings: Theory and Applications
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Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.
Galois Theory: The Galois Correspondence
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Explores the Galois correspondence and solvability by radicals in polynomial equations.
Decomposition & Inertia: Group Actions and Galois Theory
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Explores decomposition groups, inertia subgroups, Galois theory, unramified primes, and cyclotomic fields in group actions and field extensions.
Ramification and Structure of Finite Extensions
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Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.
Galois Theory of Qp
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Explores the Galois theory of Qp, covering algebraic extensions, inertia groups, and cyclic properties.
Finite Extensions of Qp: Local Constancy
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Discusses the classification of finite extensions of Qp and introduces Krassner's Lemma on root continuity.
Galois Theory: Extensions and Residual Fields
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Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.
Frobenius Theorems in Number Theory
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Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.
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.
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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