Solution
= Solution
The <idele group> is
$$
\mathbb I_K=\prod_v'K_v^\times
=\left\{(x_v)_v:x_v\in\mathcal O_v^\times
\text{ for all but finitely many finite }v\right\},
$$
the restricted product with respect to the local unit groups.
= Solution
The <idele group> is
$$
\mathbb I_K=\prod_v'K_v^\times
=\left\{(x_v)_v:x_v\in\mathcal O_v^\times
\text{ for all but finitely many finite }v\right\},
$$
the restricted product with respect to the local unit groups.