Question: Why was there a collapse in authority in the Greek peninsula in the 7th century?
About the article "Greece", section "Medieval period (4th century–1453)".

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Medieval period (4th century–1453).
The Roman Empire in the east, following the fall of the Empire in the west in the 5th century, is conventionally known as the Byzantine Empire (but was simply called "Roman Empire" in its own time) and lasted until 1453.
With its capital in Constantinople, its language and literary culture was Greek and its religion was predominantly Eastern Orthodox Christian.
From the 4th century, the Empire's Balkan territories, including Greece, suffered from the dislocation of the "Barbarian Invasions".
The raids and devastation of the Goths and Huns in the 4th and 5th centuries and the Slavic invasion of Greece in the 7th century resulted in a dramatic collapse in imperial authority in the Greek peninsula.
Following the Slavic invasion, the imperial government retained control of only the islands and coastal areas, particularly cities such as Athens, Corinth and Thessalonica, while some mountainous areas in the interior held out on their own and continued to recognize imperial authority.
Outside of these areas, a limited amount of Slavic settlement is generally thought to have occurred, although on a much smaller scale than previously thought.
The Byzantine recovery of lost provinces began toward the end of the 8th century and most of the Greek peninsula came under imperial control again, in stages, during the 9th century.
This process was facilitated by a large influx of Greeks from Sicily and Asia Minor to the Greek peninsula, while at the same time many Slavs were captured and re-settled in Asia Minor and those that remained were assimilated.
During the 11th and 12th centuries the return of stability resulted in the Greek peninsula benefiting from strong economic growth – much stronger than that of the Anatolian territories of the Empire.
Following the Fourth Crusade and the fall of Constantinople to the "Latins" in 1204 most of Greece quickly came under Frankish rule (initiating the period known as the "Frankokratia") or Venetian rule in the case of some of the islands.
The re-establishment of the Byzantine Empire in Constantinople in 1261 was accompanied by the recovery of much of the Greek peninsula, although the Frankish Principality of Achaea in the Peloponnese remained an important regional power into the 14th century, while the islands remained largely under Genoese and Venetian control.
In the 14th century much of the Greek peninsula was lost by the Empire as first the Serbs and then the Ottomans seized imperial territory.
By the beginning of the 15th century, the Ottoman advance meant that Byzantine territory in Greece was limited mainly to the Despotate of the Morea in the Peloponnese.
After the fall of Constantinople to the Ottomans in 1453, the Morea was the last remnant of the Byzantine Empire to hold out against the Ottomans.
However, this, too, fell to the Ottomans in 1460, completing the Ottoman conquest of mainland Greece.
With the Turkish conquest, many Byzantine Greek scholars, who up until then were largely responsible for preserving Classical Greek knowledge, fled to the West, taking with them a large body of literature and thereby significantly contributing to the Renaissance.
Named in the classical tradition.
Zaleucus (Ancient Greek: Ζάλευκος; fl.
7th century BC) was a Greek lawgiver. 
Slavic invasions and settlements.
From 27 BC until the end of the 6th century, the Peloponnese formed part of the province of Achaea, which during Late Antiquity comprised also the eastern parts of Central Greece.
Its capital was Corinth.
From the 580s on, as attested in the "Chronicle of Monemvasia", the Slavic invasions which affected the wider Balkans reached the peninsula, and led to the abandonment of the urban centres of Antiquity in favour of either remote or offshore locations like Monemvasia, while the inhabitants of several cities such as Patras are claimed by the "Chronicle" to have emigrated to Italy altogether.
Along with statements by medieval chroniclers like Isidore of Seville and Constantine Porphyrogennetos that Greece had completely submitted to the Slavs, this led to assumptions by earlier scholars that collapse of Byzantine control was total, and that the Peloponnese remained outside imperial control for two centuries afterwards.
The literary evidence is partially confirmed by several buried coin hoards from the 570s/580s and early 7th century, which attest to large-scale upheaval in two waves, one that peaked ca.
587, the date provided by the "Chronicle", and one that peaked in the far larger crisis of the reign of Heraclius (r. 610–641).
Literary, toponymic and archaeological evidence on the other hand shows that the Slavic invaders settled mostly in the western half of the peninsula, i.e.
the fertile plains of Elis and Messenia, Achaea and the plateau of Arcadia, while Byzantine authority survived in the more mountainous eastern parts of the peninsula as well as in various outposts around the coast, including Patras.
Nevertheless, as the rapid-re-Hellenization of the peninsula in the 9th century shows, a large Greek-speaking population must have remained in the areas overrun by the Slavs. 
The area remained part of the Byzantine empire until the late early 7th century when the Slavic migration destroyed Byzantine authority in most of the Balkan peninsula.
Since then Dardania ceased to exist as separate administrative entity. 
Panticapaeum () was an important ancient Greek city on the eastern shore of Taurica, which is now the Crimean peninsula.
The city was built on Mount Mithridat, a hill on the western side of the Cimmerian Bosporus.
It was founded by Milesians in the late 7th or early 6th century BC.
The ruins of the site are now located in the modern city Kerch.