Desolating Sacrilege

I have been wondering about the incident of the Roman shields mentioned by Philo and believed by some scholars to be the reference to the “desolating sacrilege” mentioned in Matthew 24:15 and Mark 13:14. Why is it that Luke does not include in Luke 21:20-24: “But when you see the desolating sacrilege set up where it ought not to be?”

Can it be shown that Luke did not mention the “desolating sacrilege” because the incident of the shields and/or Caligula occurred after the crucifixion?

Other scholars cite the intention of Caligula to install his statute in the Temple as the “desolating sacrilege.”

Is this evidence that the Lucan pericope is the earliest or based on an earlier more accurate tradition than that utilized by Matthew and Mark?

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