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In a famous paper

Hartshorne - Varieties of small codimension,

Hartshorne formulates a conjecture, which roughly says that varieties of small codimension in projective space are complete intersections.

On page 1023, he mentions a positive result which he has proved on this conjecture, which uses the Chebotarev density theorem (!). It says that this result is to appear in a paper

Hartshorne - Projective varieties of small degree.

I'm having difficulty finding this paper. Did it ever appear in print? Have similar results been proved elsewhere using the same/different methods? As a number theorist, the use of the Chebotarev density theorem here greatly interests me, and I would be interested in seeing the proof with this method if it exists.

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    $\begingroup$ In the book "Algebraic geometry", Arcata 1974 he says that it is unpublished (page 162): books.google.at/books?isbn=082181429X. $\endgroup$
    – Dietrich Burde
    Commented Feb 12, 2014 at 10:53
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    $\begingroup$ The footnote on page 1024 lets suspect that Hartshorne did not want to publish it. $\endgroup$
    – ACL
    Commented Feb 12, 2014 at 11:24
  • $\begingroup$ It may be worth contacting Hartshorne himself, even though he might prefer not to deal with this by now. $\endgroup$
    – Jim Humphreys
    Commented Feb 13, 2014 at 17:33

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