Full title: Total COVID-19 Mortality in Italy: Excess Mortality and Age Dependence through Time-Series Analysis.
tl;dr
estimated fatalities from excess mortality in Italy: 52,000 ± 2000. Population fatality Rate: 0.22% in Lombardia (0.57% in the most affected towns) which put a lower bound on the IFR. Infection rate probably 60-70% in the most affected towns and herd immunity should now be present.
I think they might be overestimating the infection rate though (but then again, they have huge error bars).
They use the PFR computed from the excess mortality (which is fine), but that includes a lot of people that have died on their home, which were more probably more likely to die (but with an unknown factor) that those that died in an hospital (whose CFR can be estimated). But they use the CFR from Princess Diamond, correcting for the age group but not for the fact that all the cases form Princess Diamond were treated in an hospital.
It is probably not a big deal as the major result of the paper is an estimation of the PFR.
tl;dr
estimated fatalities from excess mortality in Italy: 52,000 ± 2000. Population fatality Rate: 0.22% in Lombardia (0.57% in the most affected towns) which put a lower bound on the IFR. Infection rate probably 60-70% in the most affected towns and herd immunity should now be present.