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I recall seeing a hand-drawn picture of spec of a ring (maybe of $\mathbb Z$?) that had been passed around in the early days of the Zariski topology. Does anyone know where I can find a copy?

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I think you mean this image by Mumford.

spec Z[x] by Mumford

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  • $\begingroup$ That's it! Thanks so much. $\endgroup$ – Josh Guffin Nov 4 '10 at 0:13
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    $\begingroup$ More informative link at the same site: neverendingbooks.org/index.php/mumfords-treasure-map.html . This contains the essay on "Mumford's treasure map" cited in the other answer. $\endgroup$ – T.. Nov 4 '10 at 0:33
  • $\begingroup$ The link in the previous comment is dead, here's a new link from the same web site. $\endgroup$ – Lee Mosher Feb 20 at 18:05
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You are thinking of the picture of Spec($Z[X]$) in Mumford's Red Book of Varieties and Schemes. A reproduction is downloadable at the link posted in the other answer, and other (less famous) pictures of prime spectra appear in the Eisenbud and Harris introductory book on schemes.

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Be sure not to miss this very interesting paper (in English) on "Mumford's treasure map" and related concepts: Lieven Le Bruyn: Un dessins d'enfants

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