Ramification Theory: Dedekind Recipe

This lecture covers the ramification theory in algebraic number theory, focusing on the definition of ramified primes, discriminant ideals, and the behavior of residue fields. It also delves into Galois extensions, decomposition and inertia groups, and the Galois correspondence. The instructor explains the decomposition group, stabilizer of ideals, and reduction modulo actions. The lecture concludes with theorems and corollaries related to Galois extensions and unramified primes.