Decomposition & Inertia: Group Actions and Galois Theory

This lecture covers the concepts of decomposition groups, inertia subgroups, and Galois theory. It explains how the group G acts transitively on Specp(B), the decomposition group of P, and the Frobenius element at P. The lecture also discusses unramified primes, residual extensions, and Chebotareff's theorem. Furthermore, it explores cyclotomic fields, abelian Galois extensions, and the Frobenius elements generating Gal(K/Q). The instructor demonstrates proofs related to Galois extensions, Frobenius elements, and unramified primes, providing examples and theoretical explanations throughout the lecture.