On a cobblestone-paved square in the ancient town of Tivoli, north-east of Rome, in late September, a large crew is prepping to shoot a key scene in Italian period drama “La Storia,” which will be pubcaster RAI’s biggest event show next year.

Based on a bestselling novel by the late great Elsa Morante – whom “My Brilliant Friend” author Elena Ferrante often cites as her primary literary reference – “La Storia” is set during the final years of World War II and its immediate aftermath in Italy...