Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 123 / 4 / 1 / b

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- Solution b

Solution

The idele group is

I_{K} = \prod_{v}^{'} K_{v}^{\times} = {(x_{v})_{v} : x_{v} \in O_{v}^{\times} for all but finitely many finite v},

the restricted product with respect to the local unit groups.

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