Missing exposes in SGA 5, and the composition of the SGA's 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?
 A: 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:

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*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.

A: "It was a unique phenomenon of research and publication outside of the main mathematical journals that ran from 1960 to 1969 at the IHÉS near Paris.[...] The seminar notes were eventually published in twelve volumes, all except one in the Springer Lecture Notes in Mathematics series". SGA, Wikipedia.
In regard of SGA1 expose VII "n'existe pas":
"Ayant à rédiger l'exposé VII du Séminaire de Géométrie Algébrique de l'IHES de 1961, qui devait être consacré au formalisme général de la théorie de la descente, nous avons été conduit, et même poussé, à y inclure un certain nombre de considérations qui n'ont qu'un rapport lointain avec la Géométrie. C'est une des raisons pour lesquelles ce travail est présenté de manière autonome, l'autre étant sa date d'achèvement. La Géométrie Algébrique moderne faisant grand usage des techniques de descente, il est bon qu'elles soient exposées en détail. C'est aussi la raison pour laquelle nous ne donnons que peu d'exemples: on en trouvera dans le séminaire susnommé et dans celui de 1963". Méthode de la descente, J. Giraud.
I see the SGAs as divergent in nature with a complex structure not intended to be a single publication. For example, M Demazure says "actually SGA3 was a parenthesis and did not really belong to the SGA mainstream" and that could be said with the majority of the SGAs, descent (SGA I) could be re-studied with topos theory (SGA IV) and also Galois theory, multigaloisian topos, stacks... SGA must be seen as an unfinished work and not (as the inclusion of SGA IV 1/2 suggest) a completed work. A work that requires left aside concepts and approaches for the more natural ones, always searching the harmony. I think what is lost in SGA (due to its titanic dimension) is what Pursuing stacks accomplish, namely, the process of writing a result that lately will be ameliorated (or "naturalized", "harmonized" ...) divergently.
