Lectures related to Splitting of prime ideals in Galois extensions

Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Explains the factorisation of ideals in a Dedekind ring using prime ideals and covers ramification index, residual fields, inertia degree, and properties of Dedekind rings.

Algebraic Geometry: Localization and Prime Ideals

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Factorisation in PIDs

Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.

Decomposition & Inertia: Group Actions and Galois Theory

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

Finite Extensions of Qp: Local Constancy

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

Ramification Theory: Dedekind Recipe

Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.

Frobenius Theorems in Number Theory

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Ramification Theory: Residual Fields and Discriminant Ideal

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

Separable Extensions: Dedekind Rings

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

Dimension of Algebraic Variety

Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.

Ramified Extensions: Eisenstein Polynomials

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

Cyclotomic Extensions: Norms, Ideals, and Primes

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

Dedekind Rings: Integral Extensions and Noetherian Rings

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Factorisation in Principal Ideal Domains

Explores factorisation in Principal Ideal Domains and the properties of prime numbers.

Symbolic Powers: Interpretation and Applications

Covers the interpretation and applications of symbolic powers in algebraic structures, focusing on Krull's Hauptideal Satz and Noetherian rings.

Dedekind Rings: Factorisation and Ideal Class Group

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

Localization Theorem in Dedekind Rings

Explores the Localization Theorem in Dedekind rings, isomorphism induced by injection, and ramification in field theory.

Irreducible Algebraic Sets

Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.