Grothendieck's Éléments de géométrie algébrique, also known as EGA, was originally devised to consist of thirteen volumes (as stated in the introduction of the first volume), from which Grothendieck ended up writing only the first four ones, in the period 1960-1967. They were published inside Publications mathématiques de l’I.H.É.S. A second edition of EGA I was published by Springer in 1971, but then... that was it. There was no second edition of the other EGA volumes.

My question is: why did they not proceed with the second edition of the already existing EGA volumes?

Was Grothendieck himself opposed to a second edition? Why?

  • 1
    $\begingroup$ The wikipedia article suggests that by 1970, Grothendieck had developed new tools which would have required extensive revisions to the earlier chapters. Although he did revise the first chapter for a second edition, he did not appear to have the time to revise the other chapters while at the same time continuing to develop the subject. A version of EGA V is available on the Grothendiek Circle site. $\endgroup$
    – nwr
    Commented Mar 8, 2023 at 20:56
  • $\begingroup$ What is the motivation for your question? Grothendieck left the mathematical community in 1973, after three years of militancy. For me, it is consequential after leaving the mathematical community not embarking oneself on reprinting versions or revising monumental works. Grothendieck shifted interests. $\endgroup$ Commented Mar 10, 2023 at 14:47
  • $\begingroup$ @user234212323 My question is also "why nobody tried to keep going with a second edition." I think that later some people embarked on a second edition of SGA, without Grothendieck's collaboration. I don't know whether Grothendieck himself was in charge of the second edition of EGA I published by Springer or how much he was collaborating in this project. My question is more like why nobody was interested in proceeding with a second edition of EGA. $\endgroup$ Commented Mar 10, 2023 at 16:28
  • $\begingroup$ SGA was published in the '70s because it was circulated informally in the '60s in mimeograph form (this makes an edition necessary). In the case of EGA, they are beautifully edited by the PMIHES. On the other hand, the reedition of the SGA is not working as smoothly as you think, it is tricky. The project was running only recently in the 2010s but Grothendieck declared in 2014 that he does not give permission for republication, or reedition... $\endgroup$ Commented Mar 10, 2023 at 16:44
  • $\begingroup$ By the second edition of the SMF the project stopped then at SGA 3 (out of seven). My answer to your question is that regarding the unconventional character of Grothendieck, little time has passed to have at last an idea of his complete works, or a publication of them thereof. $\endgroup$ Commented Mar 10, 2023 at 16:44


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