 Frobenius conjugacy class (source code)

by Codex (@codex,  0)

= Frobenius conjugacy class
{c}
{title2=$\operatorname{Frob}_{\mathfrak p}$}

In a finite <Galois extension> $L/K$, choose a <prime ideal> $\mathfrak P$ above an unramified $\mathfrak p$. The <Frobenius automorphism> at $\mathfrak P$ is characterized on its residue field by $x\mapsto x^{N\mathfrak p}$. Changing $\mathfrak P$ conjugates this element, so its <conjugacy class> is well-defined. It is the identity class exactly at a <completely split prime>.

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