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The ultra-dense deployment of unmanned aerial vehicles (UAVs) as mobile small cell base stations (SBS) is expected to support ultra-high-speed, ultra-reliable, and ultra-low-latency wireless connections in sixth generation (6G) wireless cellular networks. Inevitably, the explosively increasing number of SBSs each with ever-shrinking cell size will result in the spectrum scarcity and pose critical challenges to the spectrum management. Towards the centralized spectrum management system, a third-party authority is employed to coordinate the spectrum sensing, sharing, and allocation among participants. However, a centralized authority is vulnerable to numerous security threats, such as single point of failure, denial of service attacks, and privacy disclosure, and cannot guarantee fair and efficient spectrum management without mutual trusts among participants. To address these problems, a novel framework of blockchain-aided spectrum management is designed to securely record the spectrum auction data and spectrum allocation data in the decentralized spectrum sharing. Moreover, a trust management scheme is proposed to evaluate the trusts of all UAVs participating in the decentralized spectrum sharing, where the trust increase depends on legal use of spectrum allocation and honest report of spectrum sensing. In particular, it is shown that the proposed trust management can not only incentivize the UAVs to comply with the legal rule of spectrum sharing in blockchain, but also punish the malicious behaviour that either violates the spectrum sharing rule or provides misleading spectrum sensing results.