The Frankish sub-kingdom of Italy, carved from the conquered Lombard realm and first held by Charlemagne's son Pepin (crowned king in 781), then by successive Carolingian and post-Carolingian claimants holding the Iron Crown at Pavia.
Continued under rival Italian and Frankish/Burgundian claimants after the direct Carolingian line died out (888, the era of the 'anarchic' Italian kings); absorbed into the German-led Holy Roman Empire when Otto I took the Italian crown (951/962).
No dedicated English-language monograph specifically on the Carolingian-era Kingdom of Italy was found on Open Library; this synthesis covers it in detail as part of the wider Carolingian partition system.