If Pilate went to purgatory that means that he went to heaven
There is no explicit mention of his name in either the Inferno or Purgatory.
The historical record is also very vague.
Several legends have emanated from Italy, including one where Tiberius recalled him to Rome after a revolt in which Roman soldiers massacred hundreds of Samaritans. Tiberius allegedly condemned Pilate to death, and Pilate killed himself.
No such thing as purgatory.