In recent years, policymakers, academics, and practitioners have increasingly called for the development of global governance mechanisms for artificial intelligence (AI). This paper considers the prospects for these calls in light of two other geopolitical trends: digital sovereignty and digital expansionism. While calls for global AI governance promote the surrender of some state sovereignty over AI, digital sovereignty and expansionism seek to secure greater state control over digital technologies. To demystify the tensions between these trends and their potential consequences, we (...) undertake a case analysis of digital sovereignty and digital expansionism in China, the European Union, and the United States. We argue that the extraterritoriality embedded in these three actors’ policies and escalatory competitive narratives, particularly those from the US, will likely undermine substantive global AI governance cooperation. However, nascent areas of alignment or compromise, notably in data governance and technical standards, could prove fruitful starting points for building trust in multilateral fora, such as the G20 or United Nations. (shrink)