Who was the roman emperor who burned the city of rome in

a. d. 64 and accused the christians of this crime?

It was Nero.

Per wikipedia:

The Great Fire of Rome erupted on the night of 18 July to 19 July, AD 64. The fire started on the slope of the Aventine overlooking the Circus Maximus.

Tacitus wrote that Nero accused Christians of starting the fire to remove suspicion from himself. According to this account, many Christians were arrested and brutally executed by "being thrown to the beasts, crucified, and being burned alive"