sentences:  After this, Byzantine authority, nominal under Lombard rule, waned further and in 774, after conquering the Lombard Kingdom of Italy, the Frankish king Charlemagne proceeded to conquer Corsica for the Frankish hegemony, the Carolingian Empire, which he was establishing in western Europe.In 806, however, the first of a series of Moorish incursions occurred from Spain.The Muslims were defeated several times by Charlemagne's lieutenants, among them his constable Burchard.