The <idele group> is the restricted product
$$
\mathbb I_K=\prod_v'K_v^\times
$$
over all places, with respect to $\mathcal O_v^\times$ at finite places. Thus an idele has a nonzero component in every completion and belongs to $\mathcal O_v^\times$ at all but finitely many finite places.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 123 / 4 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-123/4/a/solution