The factors that increased tensions between the pope and the Byzantine emperor prior to the Great Schism included:
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The Pope's Alliance with the Byzantines' Enemies, the Lombards: The Pope sought military assistance against the Lombards, who were encroaching on Papal territories. This reliance on assistance from Western powers increased tensions with the Byzantine Empire, which viewed the Pope’s actions as a betrayal of their longstanding alliance against common foes.
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The Pope's Crowning of Charlemagne as Emperor of Rome: This event in 800 AD was particularly significant. When Pope Leo III crowned Charlemagne, it established the notion of a distinct Western Roman Empire that was separate from the Byzantine Empire. This act was perceived by the Byzantine Emperor as a direct challenge to his authority and legitimacy as the ruler of the Roman Empire, which he claimed to inherit.
These points highlight how political maneuvers and alliances contributed to the growing divide between the Roman Catholic Church and the Byzantine Empire leading up to the Great Schism in 1054.