Geographically distributed database systems use remote replication to protect against regional failures. These systems are sensitive to severe latency penalties caused by centralized transaction management, remote access to sharded data, and log shipping over long distances. To tackle these issues, we present GaussDB-Global, a sharded geographically distributed database system with asynchronous replication, for OLTP applications. To tackle the transaction management bottleneck, we take a decentralized approach using synchronized clocks. Our system can seamlessly transition between centralized and decentralized transaction management, providing efficient fault tolerance and streamlining deployment. To alleviate the remote read and log shipping issues, we support reads on asynchronous replicas with strong consistency, tunable freshness guarantees, and dynamic load balancing. Our experimental results on a geographically distributed cluster show that our approach provides up to 14x higher read throughput, and 50% more TPC-C throughput compared to our baseline.