I am slowly working to prepare a paper for the Corinth in Contrast conference scheduled for the end of the September. (It's my problem that I'm working on the paper this far in advance, not yours.) It is notable that most of the scholarship of the Late Roman period in the Corinthia rooted in archaeological evidence continues to make two major arguments: (1) the Corinthia remained prosperous much longer than an earlier generation of scholars thought and (2) At some point in Late Antiquity, and through a variety of processes, the Corinthia became Christian.
The first argument is an economic version of the old "decline of the Roman Empire" debate. To simplify, this argument demonstrates that Corinth remained economically prosperous far longer than people expected. This prosperity depended upon its place within the larger economic world of the Roman Eastern Mediterranean (which included numerous other sites that continued to prosper longer than scholars have traditionally thought). The continued prosperity of Corinth and the Eastern Empire allowed for the city to continue to fulfill many functions traditionally associated with the Classical or Roman city albeit perhaps through different institutions. In other words, the city was not in decline (at least economic decline), but was undergoing changes in institutional structure. This proposition typically contributes to an updated version of the "decline of the Roman Empire" debate which centers on more qualitative arguments over continuity or change in the Roman world. Typically, scholars have continued to see prosperity in the Late Roman Corinthia well into the 6th century A.D. The evidence for this argument largely comes from revised dating of ceramics. By assigning ceramics later dates, we can not only show that trade continued later than expected, but also revise the dating of buildings and other civic activities to show that urban life continued later than expected.
The second argument is related, but largely independent from debates over prosperity in the Corinthia. Increasingly, scholars have argued that Corinth Christianized rather later than other cities. The largely 6th century date for the construction of Early Christian basilicas is the main evidence for the Christianization of Corinth at a late date. In other words, monumental architecture provides evidence for the presence of the Christian church as an institution in Corinth, and this must have represented a critical mass of Christians among the population and accelerated the conversion of lingering pagans. Some scholars have even seen the large scale and number of baptisteries around the city of Corinth (at the Lechaion, Kraneion, Skoutelas, and Kenchreai basilicas) as being a functional response to the large number of converts present in the community.
In general, there has been only minor efforts to generalize from the larger historical consequences of these two debates. The questions linked to these two positions are numerous and significant. For example, if Corinth is so deeply interconnected with the larger Mediterranean, why does it Christianize later than many other major Mediterranean urban areas? Does the relatively late date of Christianization suggest that economic ties did not facilitate cultural or religious change? Did the continue prosperity of Corinth stand so independent from imperial ties that the construction of monumental Christian architecture by the local elite did not represent a strategy to improve one's status both across the empire and at home? Did the religious ties to the west (through the position of the Church of Corinth as subordinate to the Papacy in the West) and economic and political relationship between Corinth and centers in the East?