The Exarch reference article from the English Wikipedia on 24-Apr-2004
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Exarch

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In the Byzantine Empire, an exarch was a proconsul or viceroy who governed a province at some remove from the central authorities, the Emperor and the Patriarch of Constantinople. The term usually refers to the Exarchate of Ravenna, which governed the area of Italy that remained under Byzantine control after the reconquest by Belisarius for Justinian.

The Byzantine Exarchs of Africa nominally governed Sardinia and Corsica.

The Exarchs of Ravenna

Ravenna had become the capital of the western Roman Empire in 404 under Honorius. It remained the capital of Italy under the Ostrogoths, and after the reconquest became the seat of the provincial governor (539). Ravenna remained the seat of the Exarch until the revolt of 727 over Iconoclasm. Thereafter, the growing menace of the Lombards and the split between eastern and western Christendom that Iconoclasm caused made the position of the Exarch more and more untenable. The last Exarch was killed by the Lombards in 751. See Exarchate of Ravenna.

In the Orthodox Church, an exarch is still a prelate: an inspector of monasteries or a deputy of the Patriarch.