Tim O’Neill, Atheist, Medievalist, Sceptic and amateur Historian,” answers this question on Quora. In short, he sees no reasonable basis for rejecting the crucifixion of Jesus as historical. In his own words:
The crucifixion of a minor Galilean preacher who caused a disturbance at Passover was a very insignificant event at the time, though it had a profound impact on his small group of followers. So the only references to it by non-Christians tend to be to explain who these followers revered. But the fact that the crucifixion was such an awkward element of their faith for these early Christians makes it most likely that this was a historical event, since it is extremely unlikely it’s an element that would simply be invented.
(3 min read; 685 words)