Is it permissible to break the fast with the adhan on television, or is it obligatory to follow the adhan of the nearby mosque, which is later?

The criterion for breaking the fast is the sunset, based on the Prophet's (peace be upon him) saying: "When the night approaches from this side and the day departs from this side, and the sun sets, then the fasting person has broken his fast." There is no harm in relying on the muezzin's call to prayer for breaking the fast, as it provides a strong presumption that the sun has set. If the city follows the adhan (definition) broadcast on the radio, it is preferable to rely on it because it is more accurate.