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I'm wondering to what extent is Mumford's Geometric Invariant Theory treated in the SGA volumes, and what's the Grothendieck point of view of GIT.

I looked at the TeXified and annotated version of SGA3 and found some reference to Mumford's GIT book in the modern annotation, especially in Exposé 5, quotient by groupoid. I think GIT is one of the major advances in Algebraic Geometry in Grothendieck's time, if the answer to my question is yes, then how (it is treated)? And if the answer to my question is no, then why (it is not treated)?

Also, has anyone seen Grothendieck's comments to GIT appeared somewhere?

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GIT was about formation of quotients in situations over a field. SGA3 addressed existence of quotients under much more restrictive settings but with way more general base schemes. So the answer to your question is "No, it isn't treated in there". The satisfactory general approach to existence of quotients (in an appropriate category...) only came much later in the decade, with Artin's work on algebraic spaces (and later, algebraic stacks). There may be some scattered references to GIT in bits of SGA7, but there is nothing substantial about GIT done in any of that stuff. –  BCnrd Nov 29 '10 at 6:32

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