Intermediate Coatings: Revisiting Galoisian Correspondence

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Covers the Galois correspondence, relating subgroups to intermediate fields.

Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.

Covers the uniqueness of norm extension in finite fields and the construction of norms on finite extensions of Qp.

Introduces Galois fields, elliptic curves, factorization algorithms, and the discrete logarithm problem in cryptography.

Explores Galois fields, elliptic curve cryptography, arithmetic operations, group structure, and practical examples in cryptography.

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Discusses the classification of finite extensions of Qp and introduces Krassner's Lemma on root continuity.