  We demonstrate that the experimentally observed conductance oscillations
through a gate-controlled quantum dot under quantized Hall conditions originate
from a true Aharonov-Bohm phase that is acquired by the electrons as they
co-propagate coherently through incompressible strips at a particular filling
factor and enclose a certain magnetic flux within the dot. The absence of
oscillations at certain filling factors is explained. The self-consistent
screening theory of the integer quantized hall effect reveals the range of
experimental parameters under which further intriguing oscillation patterns are
observable.
