Galois Theory of Qp

Related lectures (31)

Explores algebraic extensions, constructions, irreducible polynomials, autonomous constructions, and cutting compositions.

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

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

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

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

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

Explores quotient by Galois action, focusing on coatings, actions, and shares in various spaces.

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

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

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

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Page 2 of 2