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Crop type maps are critical for tracking agricultural land use and estimating crop production. Remote sensing has proven an efficient and reliable tool for creating these maps in regions with abundant ground labels for model training, yet these labels remain difficult to obtain in many regions and years. NASA's Global Ecosystem Dynamics Investigation (GEDI) spaceborne lidar instrument, originally designed for forest monitoring, has shown promise for distinguishing tall and short crops. In the current study, we leverage GEDI to develop wall-to-wall maps of short vs tall crops on a global scale at 10 m resolution for 2019-2021. Specifically, we show that (1) GEDI returns can reliably be classified into tall and short crops after removing shots with extreme view angles or topographic slope, (2) the frequency of tall crops over time can be used to identify months when tall crops are at their peak height, and (3) GEDI shots in these months can then be used to train random forest models that use Sentinel-2 time series to accurately predict short vs. tall crops. Independent reference data from around the world are then used to evaluate these GEDI-S2 maps. We find that GEDI-S2 performed nearly as well as models trained on thousands of local reference training points, with accuracies of at least 87% and often above 90% throughout the Americas, Europe, and East Asia. Systematic underestimation of tall crop area was observed in regions where crops frequently exhibit low biomass, namely Africa and South Asia, and further work is needed in these systems. Although the GEDI-S2 approach only differentiates tall from short crops, in many landscapes this distinction goes a long way toward mapping the main individual crop types. The combination of GEDI and Sentinel-2 thus presents a very promising path towards global crop mapping with minimal reliance on ground data.