Lectures related to Abelian extension

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Covers the properties of finite dimensional algebras and non-semisimple representations.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Covers the damped harmonic oscillator in quantum optics, discussing alternative descriptions and extensions like finite temperature.

Covers the extension of fields, defining the norm of an element from one field to another, and introducing the p-adic valuation.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.

Explores decomposition groups, inertia subgroups, Galois theory, unramified primes, and cyclotomic fields in group actions and field extensions.

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

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

Explores right extensions in infinity category theory and their equivalent definitions.

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

Covers the concept of special open sets and epsilonization, discussing unique extensions of derivations and specific value settings.

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

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

Covers extending domains, leading coefficients, and valid extensions.

Explores the extension and properties of multiple integrals for continuous functions on rectangles.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Covers the concept of matroids, focusing on matroid intersection and the properties of subsets of a ground set.

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.