Galois Theory of Qp

This lecture covers the Galois theory of Qp, focusing on understanding algebraic extensions of Qp. The instructor explains various facts about the Galois theory at Qp, including the concept of inertia groups and cyclic properties. The lecture delves into the relationship between Galois extensions and residue fields, highlighting the complexity and uniqueness of certain groups. Additionally, the discussion extends to local and global fields, emphasizing the significance of complete fields in the context of Galois theory. The session concludes with insights into Krasner's Lemma and its applications, showcasing the independence of arguments from specific fields like Qp.