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Oct 5, 2013 at 19:25 comment added Martin Brandenburg The reconstruction works for Durov's schemes if you take into account the tensor structure (arxiv.org/abs/1202.5147).
Jul 29, 2010 at 11:20 comment added Zoran Skoda You can construct some space, but the spectrum will be too small to recover the original scheme; so it is not a reconstruction.
Jul 28, 2010 at 5:22 comment added Shizhuo Zhang Zoran, can we do reconstruction theorem using category of vector bundles on some schemes?, i.e. Vect(X), it is an exact category
Jul 27, 2010 at 14:36 comment added Shizhuo Zhang very helpful! I am also thinking about whether Rosenberg's spectrum of right exact category gives this reconstruction theorem.
Jul 27, 2010 at 14:35 vote accept Shizhuo Zhang
Jul 27, 2010 at 14:16 history answered Zoran Skoda CC BY-SA 2.5