If you are interested in the questions surrounding the authorship, dating, and audience of the Petrine Epistles, I have compiled my own lecture notes here and most major commentaries will have full discussions on these matters. The question is what is meant by the greetings sent from “Babylon” in 1 Peter 5:13? Virtually no modern commentators see this as a literal reference to Babylon in Iraq, though the late Thomas Oden made the case that it was the Babylon of Egypt here. The vast majority of commentators argue that this was a cipher for Rome; like the Babylonian Empire of old, the Roman Empire was a world power, oppressed the people of God, and destroyed the Jerusalem temple in 70 CE as Nebuchadnezzar II had in 587 BCE (see also Revelation 17-18). Perhaps if this was an authentic letter from Peter, Peter was already using “Babylon” as a code name for Rome back in the 60s before he was executed under the order of emperor Nero. If the letter was “pseudonymous” or written by a Christian seeking to preserve Peter’s legacy after the apostle’s death, there may be a couple of ways to take this reference. Some scholars take this as indicating that the letter was sent from Christians upholding the apostolic faith, or even from a Petrine circle or school in Rome, while others argue that this is part of the fictitious setting of the letter presupposing the memory that Peter ended his life in Rome. The last option that has been entertained by Otto Zwierlein is that “Babylon” is not a reference to Rome at all, but to the metaphorical status of Christians as exiles and aliens, separated from their true homeland in heaven here. Depending on how one interprets this verse, 1 Peter 5:13 might possibly be the oldest textual reference to the social memory of Peter’s ministry in Rome.