How would the Jewish authorities have treated Jesus' corpse?

Answer:

To bury the body of a crucified individual (or anyone else) was a matter of obeying God's commandments. Joseph of Arimathaea (or whatever his name) was probably the Sanhedrin burial agent whose task it was to take care of the crucified once they had died. The approach of the Sabbath and the concern that a corpse not be left hanging after sunset (Deuteronomy 21:23) added to Joseph's concern to get the body of Jesus (and the 5 two victims) buried before sunset. Perhaps there was a Roman concession to local religious custom concerning a corpse hanging overnight, especially at the onset of the Sabbath or a festival. Joseph complied with the Torah's requirement even though he may have had no personal reason to honor the crucified individual. One may assume that if it is true that two other individuals were crucified along with Jesus and died that same day that Joseph also asked for their bodies and buried them as well.