Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 123 / 2 / a / Solution

For an unramified prime $\mathfrak{p}$ of $K$ and a prime $\mathfrak{P}$ of $L$ above it, the Frobenius automorphism is characterized byIn an abelian extension it is independent of $\mathfrak{P}$. This element is the Artin symbol