My brother and I inherited a house when our parents died. My brother refuses to pay his share of the property tax. Are we in solidarity and do I have to pay for it?

No. The tax administration has specified ( that there was no solidarity between the co-owners concerning the payment of property taxes and that therefore, only the amount of the property tax corresponding to its share in the indivision can be asked of each co-indivisary. So you do not have to pay for your brother.