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Jul 1, 2017 at 13:29 comment added R. van Dobben de Bruyn What does it mean to 'reconstruct the differential sheaf directly' if you don't know what $X$ is? I don't think this is what the OP is asking. (Although maybe 'anabelian reconstruction' is all the OP is looking for.)
Jun 29, 2017 at 11:58 history answered Myshkin CC BY-SA 3.0