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As for Saavedra's thesis, I would find it extremely naive to believe that what Grothendieck states is totally false and that one would have to ignore what he says and talk to Deligne to "know the true story". Come on. Grothendieck and Deligne both are human beings. Ditto for Saavedra, Serre, Cartier, &c. Life is more complicated than mathematics.
As often when talking about "Récoltes et semailles", I think the discussion seems to get somewhat more passionate than it should, and thus perhaps inadequate for MO. Still, people who have read the whole text should have noticed that, from the very beginning, Grothendieck states that some assertions he has made hundreds of pages later are wrong. This is related to the story surrounding Mebkhout's thesis rather than Saavedra's one, but I think it is worth mentioning in the light of what is often said of this text. (Including in comments above.) (Continued.)
Actually, it does not seem so strange to me now that the story should be related to Saavedra, since Grothendieck is talking (if I am not mistaken) about a thesis which does not satisfies him at the time of his writing. But then what is that letter I recall? Sorry for my blurred memory. I have lost my electronic copy of Récoltes & semailles.
« [Grothendieck] admits that he was at Saavedra's PhD defense, did not notice the mistake and that he has no recollection of it all anyway (even of being there). » I recall a similar story, but I am surprised this is related to Saavedra. (I thought the story I had in mind was related to Berthelot or rather Jouanolou, who later sent a letter going along the line "Pour autant que j'aie pu le constater, tous les membres du jury étaient présents".) Can you give a reference and citations? May I ask a similar request as regards "borderline psychotic accusations"? (I do not know what it means.)