Lecture
Ramification Theory: Residual Fields and Discriminant Ideal
Description
This lecture covers the ramification index, residual fields, inertia degree, and the discriminant ideal in the context of algebraic number theory. It explains the concepts of reduced algebras, ramification in field extensions, and the finite set of ramified primes. The instructor discusses the discriminant ideal of a Dedekind ring, separable extensions, and the properties of residue fields. The lecture concludes with the converse hypothesis regarding perfect residue fields and the ramification of primes.
This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.
Watch on MediaspaceOfficial source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related lectures (45)
Weyl character formula
Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.
Finite Fields: Construction and Properties
Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.
Classification of Extensions
Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.
Dimension Theory of Rings
Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.
Rings and Fields: Principal Ideals and Ring Homomorphisms
Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.