Decomposition & Inertia: Group Actions and Galois Theory

Related lectures (32)

Explores the definition of Q_p and the completion of Q,1(p) to form Qp.

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

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

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

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

Explores ramified extensions and Eisenstein polynomials, showcasing their applications in mathematical contexts.

Introduces algebras over a field, k-linear endomorphisms, and commutative algebras.

Covers the algebraic closure of Qp and the definition of p-adic complex numbers, exploring roots' continuous dependence on coefficients.

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

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

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

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

Page 2 of 2