Ramification and Structure of Finite Extensions

This lecture covers the ramification and structure of finite extensions of Qp. It explains the integral closure of Zp in K, the unique maximal ideal in A, and the form of any ideal in A. The lecture also discusses the finite extension of Qp, the ramification index, and unramified extensions. Additionally, it delves into the Galois property of certain extensions and the concept of Eisenstein polynomials. The instructor demonstrates the relationship between uniformizers, residue fields, and the structure of finite extensions, providing examples and proofs along the way.