MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
I marvel at that, when looking at SGA, you end up marveling at its «poor construction» of all things! – Mariano Suárez-Alvarez Oct 20 '10 at 17:50
The SGA's are thousands of pages written by a large number of people, worked out over a series of years, presented in a series of seminars, typed up by a series of typists. I don't know, but I can well imagine, that some exposes were lost (in that the paper manuscripts were lost), others were never written, and others were written but not typed. To get some sense of the atmosphere surrounding their writing, you can read this interview with Luc Illusie. – Emerton Oct 20 '10 at 19:12
In the note, Daniel Ferrand explains why the exposé XI of SGA 6, of which he was in charge, is missing. In short, he found a problem in the exposé (due to the non additivity of the trace in derived categories), which would have forced him to redo everything in a new setting (using ideas of Deligne) and he somehow lost interest in it. – Jérôme Poineau Oct 20 '10 at 20:21
SGA awaits a really serious historian of mathematics. – Charles Matthews Oct 21 '10 at 8:26
In the introduction of SGA 5 Illusie explained why some exposes were removed when publishing it. One can find the missing ones at least in the math library in Orsay, in some early version of SGA's (in the form of notes). – shenghao Nov 29 '11 at 15:27

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.