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Lecture
Galois Theory of Qp
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Related lectures (31)
Bar Construction: Homology Groups and Classifying Space
Covers the bar construction method, homology groups, classifying space, and the Hopf formula.
Galois Correspondence
Covers the Galois correspondence, relating subgroups to intermediate fields.
Topology: Homomorphisms and Galois Theory
Explores homomorphisms in topology and delves into Galois theory.
Intermediate Coatings: Revisiting Galoisian Correspondence
Revisits the Galoisian correspondence and explores group actions in intermediate coatings.
Cohomology: Cross Product
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Galois Fields and Elliptic Curves
Introduces Galois fields, elliptic curves, factorization algorithms, and the discrete logarithm problem in cryptography.
Quotient by Galois Action
Explores quotient by Galois action, focusing on coatings, actions, and shares in various spaces.
Elliptic Curve Cryptography: Galois Fields
Explores Galois fields, elliptic curve cryptography, arithmetic operations, group structure, and practical examples in cryptography.
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.
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.
Galois Theory: The Galois Correspondence
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Explores the Galois correspondence and solvability by radicals in polynomial equations.
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: Solvability and Radical Extensions
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Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.
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.
Galois Theory: Dedekind Rings
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Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.
Galois Theory: Extensions and Residual Fields
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Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.
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: Dedekind Recipe
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Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.
Finite Degree Extensions
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Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.
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