Governments have begun to view AI compute infrastructures, including advanced AI chips, as a geostrategic resource. This is partly because “compute governance” is believed to be emerging as an important tool for governing AI systems. In this governance model, states that host AI compute capacity within their territorial jurisdictions are likely to be better placed to impose their rules on AI systems than states that do not. In this study, we provide the first attempt at mapping the global geography of public cloud GPU compute, one particularly important category of AI compute infrastructure. Using a census of hyperscale cloud providers’ cloud regions, we observe that the world is divided into “Compute North” countries that host AI compute relevant for AI development (ie. training), “Compute South” countries whose AI compute is more relevant for AI deployment (ie. running inferencing), and “Compute Desert” countries that host no public cloud AI compute at all. We generate potential explanations for the results using expert interviews, discuss the implications to AI governance and technology geopolitics, and consider possible future trajectories.