The government can try to ban in in their geographical jurisdiction but they can't shut down Bitcoin network because of its decentralisation functionality and nobody controls the network.Although they could try to create a situation of 51% attack by taking control of the network but for that they need to indulge in mining at huge scale with thousands of ASIC mining spread across different countries.But this is also not possible under POW algorithm because it will be very costly and still it would not be implemented.They can try to shut down the internet services but you can still sign your transaction offline but transaction will be recorded on blockchain with internet connectivity only.But will they shut down whole internet for Bitcoin only.So we can say it a currency which is not controlled by anyone irrespective of his wealth and power.