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Lecture
Finite Degree Extensions
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Related lectures (34)
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.
Elliptic Curve Cryptography: Galois Fields
Explores Galois fields, elliptic curve cryptography, arithmetic operations, group structure, and practical examples in cryptography.
Intermediate Coatings: Revisiting Galoisian Correspondence
Revisits the Galoisian correspondence and explores group actions in intermediate coatings.
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.
Finite Fields: Properties and Applications
Explores the properties and applications of finite fields, including isomorphism and cyclic 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: Extensions and Residual Fields
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Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.
Galois Theory: The Galois Correspondence
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Explores the Galois correspondence and solvability by radicals in polynomial equations.
Purely Inseparable Decompositions
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Explores purely inseparable decompositions, Galois property, and algebraic closures.
Galois Theory: Recap and Transitivity
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Covers the recap of Galois theory and emphasizes the transitivity of Galois groups.
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.
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.
Hensel's Lemma and Field Theory
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Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.
Ramification Theory: Residual Fields and Discriminant Ideal
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Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.
Dedekind Rings: Factorisation and Ideal Class Group
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Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.
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.
Galois Theory of Qp
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Explores the Galois theory of Qp, covering algebraic extensions, inertia groups, and cyclic properties.
Algebraic Extensions and Decomposition of Fok [x]
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Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].
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