I have downloaded from this link a quite poor quality scan of the letter dating May 1966 that Grothendieck sent to Tate mentioning his ideas about generalizing Monsky-Washnitzer cohomology. I am trying to put it in LaTeX, at least for my own reference. So, first of all, do you know if it ever appeared in print somewhere or if the typing has already been done by someone? And, secondly, does anyone has a better-quality file? The big problem with this is that many top and bottom lines are missing, sometimes making it impossible to reconstruct the original sentence.
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asked Jun 5, 2013 at 3:51
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1$\begingroup$ Did you ever end up writing up the letter? The link in your post doesn't seem to be working, and I can't find the letter elsewhere by googling. $\endgroup$– Dylan WilsonCommented Sep 18, 2014 at 14:39
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$\begingroup$ I finally gave up my project since the version I had of the letter is quite unreadable. That being said, I re-checked the link tonight and it works on my PC...very strange. If you still have troubles, you can contact me be e-mail and I'll send you my pdf. $\endgroup$– Filippo Alberto EdoardoCommented Sep 18, 2014 at 20:22
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$\begingroup$ weird... it works now. Maybe I had a bad internet connection, or the site was having trouble earlier. Thank you! $\endgroup$– Dylan WilsonCommented Sep 19, 2014 at 0:58
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$\begingroup$ although it looks like the top of every page is missing a line... which is unfortunate. $\endgroup$– Dylan WilsonCommented Sep 19, 2014 at 2:22
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2 Answers
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In the light of past events ("Les Archives Grothendieck"), we now have an "ameliorated" version of the letter:
Cote n° 6. Lettre Tate (mai 66) (Cristaux) : lettre (1966), tapuscrit, notes manuscrites. 1966 - [à partir de 1970].
See [here] for more.
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I don't know if this is of any use.... but I believe that the ideas in this letter were written up somewhat later in this article:
Grothendieck, A. Crystals and the de Rham cohomology of schemes. 1968 Dix Exposés sur la Cohomologie des Schémas pp. 306–358 North-Holland, Amsterdam; Masson, Paris
The article is actually some notes by Coates and Jussila of a seminar by Grothendieck. You can find a copy of the article at chapter IX of this book.
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8$\begingroup$ @Nick: Thanks. Yes, I know that paper by Grothendieck, and I agree that it morally contains the same material, expecially including connections with M-W cohomology. But I like the original one, where he also explains the choice of the noun "crystal" and it gives the feeling of listening to a phone call between friends ;-) $\endgroup$ Commented Jun 5, 2013 at 9:51