Lecture
P-adic Numbers: Completion and Norm
Related lectures (33)
Extension of Fields: Norm and Valuation
Covers the extension of fields, defining the norm of an element from one field to another, and introducing the p-adic valuation.
Norm Extension in Finite Fields
Covers the uniqueness of norm extension in finite fields and the construction of norms on finite extensions of Qp.
Topology: Homomorphisms and Galois Theory
Explores homomorphisms in topology and delves into Galois theory.
Galois Correspondence
Covers the Galois correspondence, relating subgroups to intermediate fields.
Galois Theory: Extensions and Residual Fields
Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.
Algebras and Field Extensions
Introduces algebras over a field, k-linear endomorphisms, and commutative algebras.
Dimension Theory of Rings
Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.
Ramification and Structure of Finite Extensions
Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.
Galois Theory Fundamentals
Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.
Ramification Theory: Residual Fields and Discriminant Ideal
Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.