Ramification Theory: Dedekind Recipe

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Page 3 of 4

Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.

Intermediate Coatings: Revisiting Galoisian Correspondence

Revisits the Galoisian correspondence and explores group actions in intermediate coatings.

Finite Degree Extensions

Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.

Separable Extensions: Dedekind Rings

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Factorisation in Dedekind Ring

Explains the factorisation of ideals in a Dedekind ring using prime ideals and covers ramification index, residual fields, inertia degree, and properties of Dedekind rings.

Localization Theorem in Dedekind Rings

Explores the Localization Theorem in Dedekind rings, isomorphism induced by injection, and ramification in field theory.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Integral Representations: Quadratic Lattices and Hasse Principle

Explores integral representations, quadratic lattices, and the Hasse Principle.

Galois Fields and Elliptic Curves

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