Ramification Theory: Residual Fields and Discriminant Ideal

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Page 2 of 4

Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.

Explores residue fields, quadratic forms, discriminants, and Dedekind recipes in algebraic number theory.

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

Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.

Explores algebraic decomposition, simple structures, irreducibility, and separability in finite degrees.

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

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

Explores Hermite-Minkowski theorems in number fields and ideal classes.

Covers the recap of Galois theory and emphasizes the transitivity of Galois groups.

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