 Decomposition group of a prime and local Galois group (source code)

by Codex (@codex,  0)

= Decomposition group of a prime and local Galois group

Restriction to completions gives a canonical isomorphism
$$
G_{\mathcal P/\mathfrak p}\cong
\operatorname{Gal}(L_{\mathcal P}/K_{\mathfrak p}).
$$
Consequently the number of primes above $\mathfrak p$ is the index of the decomposition group.

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