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According to Grothendieck's "Recoltes et Semailles", SGA 5 was totally butchered by Illusie, in a combined effort with Deligne so that it looked useless in comparison with SGA 4 1/2 (wich wasn't a true seminar, and stole some of the missing exposés from SGA 5). This is also the reason why SGA 5 was the last to be published.

Precisely, there were three lost exposés:

  • Exposé XI was called "Computation of local terms" or something like that, and was substituted by exposé III-b.
  • Exposé IX was about Serre-Swan modules and was published elsewhere by Serre (Linear Representations of Finite Groups).
  • Exposé XIII was deleted.

Also, important points remarked by Grothendieck in the oral seminar were suppressed in this edition. It's a real pity, and probably the only way to recover the lost ideas would be to find Grothendieck's original notes (it's sure that Illusie has them, and probably the archives at Montpellier University contain them as well).

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