The Great Persecution
The Roman Emperor Diocletian came to power in 284 AD. Diocletian was an army general, and he felt that a lot of the empire's problems could be solved by not allowing so much freedom, but instead having everyone do the same thing, the right way (his way). First he was busy fighting the Germans and the Sassanids and having civil wars, then for a while he was busy trying to fix the economy.
But by 301 AD Diocletian had noticed that there were people who had different religions in the Roman Empire. Diocletian HATED this idea. First of all, these people were different from him, which seemed disrespectful. Second, they might be making the gods mad. So they had to be stopped. First Diocletian got rid of the Manichaeans.
Diocletian's palace at Split (the bell tower was added later)
Then (since that had gone pretty well), in 303 AD
he began a big persecution of the Christians.
This didn't go as well. Diocletian's co-emperors in the West weren't very interested in killing Christians, so a lot of Eastern Christians just moved to the West. Also, even Diocletian didn't really want to kill a whole lot of people. He just wanted them to worship his gods. He didn't really know what to do with the ones who said no.
Even after Diocletian retired in 305 AD, his successor, Galerius, still persecuted the Christians, but still without getting rid of them.