When a government runs a surplus then

they can say they have a balanced budget

they can reduce the national debt

they must issue more bonds to the public

they must print more money

Running government budget deficit today indicates

taxes likely will decrease in the future

government spending likely will increase in the future

investment likely will decrease in the future

nothing will happen in the future

A rising debt to GDP ratio could be since

economic activity in the economy is decreasing

the government is increasing taxes

the government is running budget surpluses

the Central bank is borrowing money

All else the same an increase in nominal GDP will

not affect the debt to GDP ratio

decrease the debt to GDP ratio

increase the debt to GDP ratio