Cooperative perception is the key approach to augment the perception of connected and automated vehicles (CAVs) toward safe autonomous driving. However, it is challenging to achieve real-time perception sharing for hundreds of CAVs in large-scale deployment scenarios. In this paper, we propose AdaMap, a new high-scalable real-time cooperative perception system, which achieves assured percentile end-to-end latency under time-varying network dynamics. To achieve AdaMap, we design a tightly coupled data plane and control plane. In the data plane, we design a new hybrid localization module to dynamically switch between object detection and tracking, and a novel point cloud representation module to adaptively compress and reconstruct the point cloud of detected objects. In the control plane, we design a new graph-based object selection method to un-select excessive multi-viewed point clouds of objects, and a novel approximated gradient descent algorithm to optimize the representation of point clouds. We implement AdaMap on an emulation platform, including realistic vehicle and server computation and a simulated 5G network, under a 150-CAV trace collected from the CARLA simulator. The evaluation results show that, AdaMap reduces up to 49x average transmission data size at the cost of 0.37 reconstruction loss, as compared to state-of-the-art solutions, which verifies its high scalability, adaptability, and computation efficiency.