Question: Where was the headquarters of the state where barbarian invaders established kingdoms?

full_context: Document 1: East–West Schism: In 476, when the last emperor of the western part of the Roman Empire was deposed and the western imperial insignia were sent to Constantinople, there was once again a single Roman Emperor. However, he had little power in the West, which was ruled almost entirely by various Germanic tribes. In the opinion of Randall R. Cloud, the permanent separation of the Greek East from the Latin West was ``the fundamental reason for the estrangement that soon followed between the Greek and the Latin Christians ''.
Document 2: Middle Ages: Roman city life and culture changed greatly in the early Middle Ages. Although Italian cities remained inhabited, they contracted significantly in size. Rome, for instance, shrank from a population of hundreds of thousands to around 30,000 by the end of the 6th century. Roman temples were converted into Christian churches and city walls remained in use. In Northern Europe, cities also shrank, while civic monuments and other public buildings were raided for building materials. The establishment of new kingdoms often meant some growth for the towns chosen as capitals. Although there had been Jewish communities in many Roman cities, the Jews suffered periods of persecution after the conversion of the empire to Christianity. Officially they were tolerated, if subject to conversion efforts, and at times were even encouraged to settle in new areas.
Document 3: Middle Ages: The invasions brought new ethnic groups to Europe, although some regions received a larger influx of new peoples than others. In Gaul for instance, the invaders settled much more extensively in the north-east than in the south-west. Slavic peoples settled in Central and Eastern Europe and the Balkan Peninsula. The settlement of peoples was accompanied by changes in languages. The Latin of the Western Roman Empire was gradually replaced by languages based on, but distinct from, Latin, collectively known as Romance languages. These changes from Latin to the new languages took many centuries. Greek remained the language of the Byzantine Empire, but the migrations of the Slavs added Slavonic languages to Eastern Europe.
Document 4: Middle Ages: Religious beliefs in the Eastern Empire and Iran were in flux during the late sixth and early seventh centuries. Judaism was an active proselytising faith, and at least one Arab political leader converted to it. Christianity had active missions competing with the Persians' Zoroastrianism in seeking converts, especially among residents of the Arabian Peninsula. All these strands came together with the emergence of Islam in Arabia during the lifetime of Muhammad (d. 632). After his death, Islamic forces conquered much of the Eastern Empire and Persia, starting with Syria in 634–635 and reaching Egypt in 640–641, Persia between 637 and 642, North Africa in the later seventh century, and the Iberian Peninsula in 711. By 714, Islamic forces controlled much of the peninsula in a region they called Al-Andalus.The Islamic conquests reached their peak in the mid-eighth century. The defeat of Muslim forces at the Battle of Tours in 732 led to the reconquest of southern France by the Franks, but the main reason for the halt of Islamic growth in Europe was the overthrow of the Umayyad Caliphate and its replacement by the Abbasid Caliphate. The Abbasids moved their capital to Baghdad and were more concerned with the Middle East than Europe, losing control of sections of the Muslim lands. Umayyad descendants took over the Iberian Peninsula, the Aghlabids controlled North Africa, and the Tulunids became rulers of Egypt. By the middle of the 8th century, new trading patterns were emerging in the Mediterranean; trade between the Franks and the Arabs replaced the old Roman economy. Franks traded timber, furs, swords and slaves in return for silks and other fabrics, spices, and precious metals from the Arabs.
Document 5: Western world: The geopolitical divisions in Europe that created a concept of East and West originated in the Roman Empire. The Eastern Mediterranean was home to the highly urbanized cultures that had Greek as their common language (owing to the older empire of Alexander the Great and of the Hellenistic successors), whereas the West was much more rural in its character and more readily adopted Latin as its common language. After the fall of the Western Roman Empire, Western and Central Europe were substantially cut off from the East where Byzantine Greek culture and Eastern Christianity became founding influences in the Arab / Muslim world and among the Eastern and Southern Slavic peoples. Roman Catholic Western and Central Europe, as such, maintained a distinct identity particularly as it began to redevelop during the Renaissance. Even following the Protestant Reformation, Protestant Europe continued to see itself as more tied to Roman Catholic Europe than other parts of the perceived civilized world.
Document 6: Middle Ages: Depopulation, deurbanisation, invasion, and movement of peoples, which had begun in Late Antiquity, continued in the Early Middle Ages. The barbarian invaders, including various Germanic peoples, formed new kingdoms in what remained of the Western Roman Empire. In the 7th century, North Africa and the Middle East—once part of the Eastern Roman Empire—came under the rule of the Caliphate, an Islamic empire, after conquest by Muhammad's successors. Although there were substantial changes in society and political structures, the break with Antiquity was not complete. The still-sizeable Byzantine Empire survived in the east and remained a major power. The empire's law code, the Code of Justinian, was rediscovered in Northern Italy in 1070 and became widely admired later in the Middle Ages. In the West, most kingdoms incorporated the few extant Roman institutions. Monasteries were founded as campaigns to Christianise pagan Europe continued. The Franks, under the Carolingian dynasty, briefly established the Carolingian Empire during the later 8th and early 9th century. It covered much of Western Europe, but later succumbed to the pressures of internal civil wars combined with external invasions—Vikings from the north, Magyars from the east, and Saracens from the south.
Document 7: Southern Europe: During the Middle Ages, the Eastern Roman Empire survived, though modern historians refer to this state as the Byzantine Empire. In Western Europe, Germanic peoples moved into positions of power in the remnants of the former Western Roman Empire and established kingdoms and empires of their own.
Document 8: Middle Ages: The Islamic conquests reached their peak in the mid-8th century. The defeat of Muslim forces at the Battle of Poitiers in 732 led to the reconquest of southern France by the Franks, but the main reason for the halt of Islamic growth in Europe was the overthrow of the Umayyad dynasty and its replacement by the Abbasid dynasty. The Abbasids moved their capital to Baghdad and were more concerned with the Middle East than Europe, losing control of sections of the Muslim lands. Umayyad descendants took over the Iberian Peninsula, the Aghlabids controlled North Africa, and the Tulunids became rulers of Egypt. By the middle of the 8th century, new trading patterns were emerging in the Mediterranean; trade between the Franks and the Arabs replaced the old Roman patterns of trade. Franks traded timber, furs, swords and slaves in return for silks and other fabrics, spices, and precious metals from the Arabs.
Document 9: Middle Ages: The migrations and invasions of the 4th and 5th centuries disrupted trade networks around the Mediterranean. African goods stopped being imported into Europe, first disappearing from the interior and by the 7th century found only in a few cities such as Rome or Naples. By the end of the 7th century, under the impact of the Muslim conquests, African products were no longer found in Western Europe. The replacement of goods from long-range trade with local products was a trend throughout the old Roman lands that happened in the Early Middle Ages. This was especially marked in the lands that did not lie on the Mediterranean, such as northern Gaul or Britain. Non-local goods appearing in the archaeological record are usually luxury goods. In the northern parts of Europe, not only were the trade networks local, but the goods carried were simple, with little pottery or other complex products. Around the Mediterranean, pottery remained prevalent and appears to have been traded over medium-range networks, not just produced locally.
Document 10: Southern Europe: The Roman Empire came to dominate the entire Mediterranean basin in a vast empire based on Roman law and Roman legions. It promoted trade, tolerance, and Greek culture. By 300 AD the Roman Empire was divided into the Western Roman Empire based in Rome, and the Eastern Roman Empire based in Constantinople. The attacks of the Germanic peoples of northern Europe led to the Fall of the Western Roman Empire in AD 476, a date which traditionally marks the end of the classical period and the start of the Middle Ages.
Document 11: Southern Europe: The period known as classical antiquity began with the rise of the city-states of Ancient Greece. Greek influence reached its zenith under the expansive empire of Alexander the Great, spreading throughout Asia.
Document 12: Southern Europe: The predominant religion is southern Europe is Christianity. Christianity spread throughout Southern Europe during the Roman Empire, and Christianity was adopted as the official religion of the Roman Empire in the year 380 AD. Due to the historical break of the Christian Church into the western half based in Rome and the eastern half based in Constantinople, different branches of Christianity are prodominent in different parts of Europe. Christians in the western half of Southern Europe — e.g., Portugal, Spain, Italy — are generally Roman Catholic. Christians in the eastern half of Southern Europe — e.g., Greece, Macedonia — are generally Greek Orthodox.
Document 13: Roman Empire: The Roman Empire was among the most powerful economic, cultural, political and military forces in the world of its time. It was one of the largest empires in world history. At its height under Trajan, it covered 5 million square kilometres. It held sway over an estimated 70 million people, at that time 21% of the world's entire population. The longevity and vast extent of the empire ensured the lasting influence of Latin and Greek language, culture, religion, inventions, architecture, philosophy, law and forms of government on the empire's descendants. Throughout the European medieval period, attempts were even made to establish successors to the Roman Empire, including the Empire of Romania, a Crusader state; and the Holy Roman Empire. By means of European colonialism following the Renaissance, and their descendant states, Greco - Roman and Judaeo - Christian culture was exported on a worldwide scale, playing a crucial role in the development of the modern world.
Document 14: Mediterranean Sea: Two of the most notable Mediterranean civilizations in classical antiquity were the Greek city states and the Phoenicians, both of which extensively colonized the coastlines of the Mediterranean. Later, when Augustus founded the Roman Empire, the Romans referred to the Mediterranean as Mare Nostrum (``Our Sea ''). For the next 400 years, the Roman Empire completely controlled the Mediterranean Sea and virtually all its coastal regions from Gibraltar to the Levant.
Document 15: Imperialism: From their original homelands in Scandinavia and northern Europe, Germanic tribes expanded throughout northern and western Europe in the middle period of classical antiquity; southern Europe in late antiquity, conquering Celtic and other peoples; and by 800 CE, forming the Holy Roman Empire, the first German Empire. However, there was no real systemic continuity from the Western Roman Empire to its German successor which was famously described as "not holy, not Roman, and not an empire", as a great number of small states and principalities existed in the loosely autonomous confederation. Although by 1000 CE, the Germanic conquest of central, western, and southern Europe (west of and including Italy) was complete, excluding only Muslim Iberia. There was, however, little cultural integration or national identity, and "Germany" remained largely a conceptual term referring to an amorphous area of central Europe.
ground_truth: Rome
sub_queries: In what state did barbarian invaders establish kingdoms? Answer: the Western Roman Empire
Where was the headquarters of the Western Roman Empire ? Answer: Rome