Given two finite dimensional quiver algebras $A$ and $B$ (over a nice field in case that helps, for example a finite field).
Question: Can an there be a finite algorithm that decides whether $A$ and $B$ are derived equivalent?
I am pretty sure that at the moment no such algorithm exists but maybe in 1000 years there is such an algorithm and the above question is rather trivial. On the other hand, there might be some theoretical reason why such an algorithm can not exist.