This came up in my last game. The Imperials played Construct Death Star.

The card reads “Resolve in any remote system that does not have Rebel units.”

The hidden Rebel base was on the remote system the Imperials wants to play this card.

My question is does the Imperial player discover the hidden base location, even though the Imperial player is not lading troops on the remote planet or can he build a Death Star on top of the Rebel Base without knowing it? And if the Imperial can not construct a Death Star in this system does the player have the option to move to a different remote system after discovering the secret Rebel base is in that system?

The Imperial player does not discover the Rebel base just by placing the DSUC in that system. The unrevealed Rebel Base being in that system does not prevent the DSUC from being there.

The Rebel player could then later decide to reveal their base which would move the units from the Rebel Base space to the system. If there are space units, combat would begin and if they survive a round of combat the DSUC will automatically blow up.

The rebel base is so weird. In some situations its best to think of it in as if it was in its own pocket galaxy, far, far away from the rest of the board. But there are certain situations in which thinking this way gets you in trouble.

My question is does the Imperial player discover the hidden base location, even though the Imperial player is not lading troops on the remote planet or can he build a Death Star on top of the Rebel Base without knowing it?

The Imperial Player does not discover the hidden base and it remains hidden since there are no Imperial ground units on the space. The Death Star does start getting built there. I suspect won't last for long as its trivial for the rebellion to destroy it at the cost the Imperils knowing where your base is.

Thank you both for helping me.