TITLE: Missing exposes in SGA 5, and the composition of the SGA's
QUESTION [17 upvotes]: Over the past couple of years I had to look in SGA for various results, and I can't but marvel at how poorly constructed it is. In SGA1 expose VII "n'existe pas", SGA 1 references higher SGA's, and so forth.
My first, albeit less urgent, question is: how were these composed, and why the many missing exposes and references to future manuscripts? Were all SGA's written simultaneously? Are the missing exposes a product of type-writing it (so changing the table of contents is too much of a bother?). Were they going to write those exposes later but never did? Why didn't they?
My second question is specifically regarding the missing exposes in SGA5. In the introduction to expose XIII in SGA1 it says that it generalizes the results of SGA5 II -- one of the missing exposes! What happened there? Is there a more appropriate reference for what SGA1 expose XIII generalizes?

REPLY [7 votes]: 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 (which 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 (probably the archives at Montpellier University contain them or the IHES library).
EDIT: More about what was missing from SGA 5:

Exposé IV, about "The cohomology class associated with a cycle", was going to be redacted by Deligne, who instead included it in SGA 4 1/2, chapter 4.

A related theme covered by Grothendieck was "The homology class associated with a cycle". This was discussed throughout many exposés in the seminar, but is absent from the published book. According to ReS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.

Exposé II, as is known from the introduction to SGA 5, was reworked by Deligne and included in SGA 4 1/2 as well.