I'm looking for a reference to the fact that the category of crystals on any scheme is locally noetherian. This is stated in Gaitsgory's paper "Crystals and D-modules" but he doesn't provide a reference.

An idea of where to look would be very helpful, thanks very much.

  • 4
    $\begingroup$ The reason you don't see a proof of such a statement in Grothendieck's article (say with a quasi-coherence condition) is that in his context it is false. (Consider big direct sums.) It is also false in the general context of the article you're asking about, for the same reason. To figure out what was intended (i.e., what intended finiteness hypotheses were omitted), etc., ask the author. $\endgroup$
    – nfdc23
    Dec 31, 2015 at 17:22
  • $\begingroup$ Thanks, I removed the reference to Grotendieck's paper since it isn't true. $\endgroup$ Dec 31, 2015 at 17:33


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