This expression means with the help of somebody. In ancient Rome, it was customary to consult an augur before making important decisions. One of these Augurs was the so called Auspex, the bird-watcher, a priest who watched the flight of birds as an omen. If his observation, auspice, was favourable, he would advise that the signs indicated divine approval for a course of action. The modern meaning has no supernatural implication.

Übersetzung:

unter jemandes Auspizien oder Schirmherrschaft

Gegenteil(e)

The opposite of "to be under the auspices" is "to accomplish something without support".

Synonym(e):

You could also say: with the approval of somebody.