When does inflation reduce the public debt ratio?

It is often said that inflation reduces public debt ratios. But we need to be much more specific on two points. For inflation to reduce the public debt ratio, nominal interest rates must not follow inflation, i.e. real interest rates must fall; if the nominal interest rate follows inflation, the only factor reducing the public debt is the inflation tax, which is small. For inflation to reduce the public debt ratio, there must be a rise in the GDP deflator, and therefore a faster rise in the value of income. If there is a rise in consumer prices, not a rise in the GDP deflator due for example to a rise in the prices of imported commodities alone, there is no deleveraging. It is clear that in this case the price increase corresponds to income that is transferred to the rest of the world (purchases of imported commodities) and does not contribute to the country's income.