Idelic congruence subgroup
= Idelic congruence subgroup
{title2=$C_K(\mathfrak m)$}
The ideles congruent to one modulo $\mathfrak m$ have finite components in $1+\mathfrak p^{n_\mathfrak p}$ at primes in the finite modulus and positive components at selected real places. Their image in $C_K$ is the idelic congruence subgroup.