@Vasilas Until much later on,after the Fourth Crusade,the Eastern Romans view the term Hellenes or Greek as an insult.The term is usually used to denigrate East Roman claims of being Roman at all.It's also got some kind of pagan connotation to it.
And wow,Basil went batshit crazy in Baghdad.
@darthfanta : Yup, aware of that ( I was taught Byzantine history by a guy who was obsessed over Laskarids). But this is a 'modern' book and not a contemporary account (notice how many times the 'author' uses the word Roman to describe the Empire in updates, when he is not explicitly talking from an Islamic point by using Rum). In TTL 980s the word Roman and Rum are being used like crazy by everyone east of Italy (and some in the west too). And before this thread follows the trajectory of the polls asking about continuations of Rome, let me make my position very clear: The Byzantine Empire WAS the Roman Empire, period. The Edict of Caracalla alone is sufficient to make that a fact.
That does not however stop me from experimenting with an idea to see what would happen if the 'Byzantines' themselves became willing to abandon the Roman heritage at some point in time. I envision this will go with a sort of Hellenic/Byzantine identity developing and co-existing with the Roman one (like from OTL Fourth Crusade to Lausanne) for a long time, perhaps with some sort of major traumatic event that leads to an intellectual divorce from the west and anti-Latinism. However, come the present day I would not really expect a largely secular Greek educated class to be attached to Caesar and Scipio as much as they are attached to the idea of being Greek, leading to an ideology of 'Byzantinism' developing where they are completely willing to abandon Rome in favor of Constantinople (so to say), to view their Empire as a successor than a continuation. This book is a Byzantinists take on Later Roman History (as said in the Intro) to contrast with works that take a more 'Roman' stance, and I have been playing a lot with it.
That being said, as of 2016 TTL Empire is still officially Basileia ton Rhomaion. Non-Greeks are rather invested in keeping the mirage of multicultural OTL Rome alive over the highly Aegean/Anatolian Greek centric Byzantinist worldview. Leads to interesting politics, to say the least. Would have probably worked better for everyone if they just went with a compromise of 'Roman Empire at Constantinople' or like, but oh well.
As for Baghdad, well a lot of it is because most reliable sources are Islamic, and Shaitanama might give you an idea of how bad the PR is. There is a lot of exaggeration, falsehood (there are theories regarding how OTL Basil never blinded an army of Bulgarians), people using the unrest as a chance to commit crime, fire damage and soldiers not knowing how to properly handle urban warfare mixed with a kernel of truth (joys of writing thread as history book). Basil was too much a man of the people (proto populist?) and his army could at times resemble the Constantinopolitan mob he grew up with than a professional force, especially when he had not exactly figured out the leading thing. He got his act together by Nineveh, and afterwards the core of the Roman army acted professionally (which is why the Fatimids tried to avoid it) but there was plenty of vengeful local riff-raff to make the things go pretty badly for civilians assumed to be members of the opposition.
I would think due to the capture of the holy city and Alexandria Basil's prestige in Christendom is sky high now. How does this affect the Empire's relations with Western Christendom? Since the Great Schism has been butterflied away how does it affect the relations between the two churches?
Tzimiskes was handling it for now, not giving the next update away yet. I broke this up into the eastern and western wars to have a better narrative. Things are definitely better for inter-Church relations (Constantinople has much more power and prestige right now) but politically relations are a mess as ever (more on next update). That being said, volunteer knights had been going to Venice to join the Empire recapture the holy land and had played some role in the battle in Egypt. Most would be re-settled in the inner Levant afterwards as proto-feudal lords to reduce administrative headaches for the Empire which wants the coast over all else.
Don't think the schism would be butterflied away.The mutual excommunications of 1054 was the final straw that broke the camel's back.The schism has been developing for centuries.What all of this would mean however would be that the Eastern Church can effectively ignore the Western Church completely whereas IOTL,the Eastern Church can't do so because of the Crusades.
By the way,why did the Copts resist the Empire unlike the other Christians in Levant?
Formal schism at 1054 is butterflied away, but an overall Greek-Latin schism will happen (inevitable by this TL). Timing is crucial though: if there is no HRE strong enough for an Italian presence (see what happened to OTL Otto's II and III and combine that with a much stronger Eastern Empire) and the Empire is in the South breathing down the Papacy's neck, the Pope will be less likely to go for a full on formal schism before things get really bad (and he can relocate somewhere safe and away from the Med).
I would also not be so certain about the Eastern church completely ignoring the West (though it has a far far stronger hand to play). Rome needs manpower, and it needs it fast.
Copts: I sorta indirectly hinted at it in the TL. They have simply not lost as much as the Levantines. Egypt had been under a centralized power, which despite being under attack late in the TL did not collapse into fragments. As such, the Fatimid government is well aware of the need to keep Copts sufficiently happy to prevent rebellion (a Coptic rebellion would have sunk the Caliphate faster than a rock). This has also been drilled into its people, so that they are more into persecuting Melkites and Chalcedonians like Venetians than target the local population. The thing is, the whose collapse of Levantine society only happened because the Empire had been invading that area for decades (while nothing major happened in Egypt for a long while) and under Phokas/Tzimiskes had an aggressively anti-Muslim policy that caused distrust to grow between the groups leading to the riots etc after Baghdad ignited the powder keg. That strategy would not have worked with the Abbassids who would stabilize it the best they could by bringing in forces from elsewhere and appeasing minorities. Small local Emirates are more dependent on locals than a centralized Empire, and can act unwisely for short term benefits. Egyptian Christians are simply better off, and see no reason to rebel for heretics when their Church is in the pocket of the Caliphs.