Pope Vigilius (537–555) was appointed a deacon in Rome in A.D. 431. In the same year, the church in Rome gave the bishop of Rome (who may have had papal authority at that time, though the circumstance described on this page makes it appear that he did not) authority to appoint his own successor.
Vigilius was chosen by Boniface II to be his successor, but the general outcry against the new process caused him to withdraw his choice and to burn the decree giving him such authority. Boniface was in fact succeeded by Pope John II, who reigned for only two years, and he was followed by Agapetus I.
Agapetus made Vigilius his representative in Constantinople in 535 or 536. There the empress Theodora was stewing over the deposition of bishop Anthimus of Constantinople for embracing the monophysite heresy, condemned at the Council of Chalcedon in 451, almost a century earlier. Despite Chalcedon's condemnation, many eastern bishops still held that Jesus had but one nature, rather than both a human and divine nature.
The empress offered Vigilius—or so it is said—a large sum of money and letters and aid that would secure his appointment to the papacy if he would embrace the monophysite doctrine.
Apparently Vigilius accepted because in 537 the commander of the Byzantine army, Belisarius, secured Rome and pressured the Roman church into deposing Pope Silverius after a short 17-month reign. This happened despite the city being beseiged by the king of the Goths, who had secured Silverius' appointment in the place of Pope Agapetus I.
These sorts of political appointments, whether the politicians forced the city of Rome to abide by "official" protocol in appointing their bishop or not, establish beyond any reasonable doubt that the succession of bishops in Rome is meaningless in the eyes of God.
Of course, there's no historical basis for the authority of the papacy, anyway, but even if there was, it was long ago lost through the multitude of such unrighteous transfers of power.
Not all the Roman clergy would accept Pope Vigilius' appointment, but Vigilius had his predecessor, Silverius, imprisoned. There the treatment was so harsh that Pope Silverius soon died. After his death, just 8 months later, the clergy gave their full assent to Vigilius, thus accounting for the fact that Rome's Annuario Pontifico, the most official list of Roman popes there is, shows an 8 month overlap in their reigns.
Pope Vigilius betrayed the empress, however. He maintained a stance against the monophysites and supported the deposition of Anthimus.
One can only assume that this was done to maintain peace with his subjects in the church in Rome. Eventually, though, he was going to have to give in, as it is dangerous to anger an empress.
Finally, Justinian, the emperor, came up with an idea. He condemned three writings, which became known as "the three chapters," whose authors had been approved by the Council of Chalcedon. Justinian figured he could get away with this since these writings were seen as supporting Nestorianism, which was condemned by the Council of Ephesus in 432.
The west would have nothing of it, though, because it came to close to overthrowing the decrees of the Council of Chalcedon. Eastern bishops embraced it because many of them were already officially excommunicated for being monophysites.
Pope Vigilius sided with the western bishops, the only safe thing to do in Rome, but Justinian was less tolerant than his wife Theodora. He sent an imperial official who pulled Vigilius out of the middle of a service to go to Constantinople.
It was a difficult journey because Rome was besieged by the Goths. Vigilius was stuck in Sicily for nearly a year, and then spent the next eight years as a virtual captive in Constantinople.
Finally he could take it no longer. He agreed to the condemnation of the three chapters, but wrote a letter in defense of the Council of Chalcedon. He was able to do this by condemning the writings but not the writers.
This was enough to satisfy Emperor Justinian. Pope Vigilius was released to return to Rome in 555, but he died on the journey home.