Rome vs Constantinople

The separation of the Latin and Eastern Catholic Churches originated formally in 1054 following theological differences over hundreds of years.   In that year the Bishop of Roman excommunicated the Bishop of Constantinople, who in turn excommunicated the Bishop of Roman.  Recent efforts to resolve those differences have been successful in all but a few matters including papal primacy and the concept of purgatory.

The Church of Rome holds that the Bishop of Rome is the supreme authority in the Church of Christ.  The Eastern Church disagrees.  This doctrine evolved overtime and originated by papal declaration in the third century.  It is based on interpretations of New Testament passages on the role of St. Peter in the church.  The Patriarch of Eastern Church argued that his role was at least of equal importance (if not more so)  based in part on the role of Constantinople as the new Rome.  (Larger secular political issues of the time here?)

Similarly, the concept of purgatory, based on early Jewish ideas, evolved as Roman doctrine over centuries formalized at numerous Church synods.  The idea holds that on death we will spend time in purgatory to cleanse our remaining sins before entering heaven.  That process can be shortened by the prayers and indulgences of the living.  The Eastern Catholics agree that some process occurs after death and before heaven to cleanse our remain sins, but fire and punishment in a place or state do not take place.  Likewise, they disavow the concept of indulgences through the prayers of the livings.  Most protestants agree.