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We present a new approach, the GeoQuorums approach, for implementing atomic read/write shared memory in mobile ad hoc networks. Our approach is based on associating abstract atomic objects with certain geographic locations. We assume the existence of focal points, geographic areas that are normally "populated" by mobile nodes. For example, a focal point may be a road junction, a scenic observation point, or a water resource in the desert. Mobile nodes that happen to populate a focal point participate in implementing a shared atomic object, using a replicated state machine approach. These objects, which we call focal point objects, are prone to occasional failures when the corresponding geographic areas are depopulated. The GeoQuorums algorithm uses the fault-prone focal point objects to implement atomic read/write operations on a fault-tolerant virtual shared object. The GeoQuorums algorithm uses a quorum-based strategy in which each quorum consists of a set of focal point objects. The quorums are used to maintain the consistency of the shared memory and to tolerate limited failures of the focal point objects, which may be caused by depopulation of the corresponding geographic areas. We present a mechanism for changing the set of quorums on the fly, thus improving efficiency. Overall, the new GeoQuorums algorithm efficiently implements read and write operations in a highly dynamic, mobile network.