In Geometric Invariant Theory, by Mumford, Fogarty, and Kirwan, if there is a mention of descent theory, it almost always comes along with a reference to SGA 8, Theorem 5.2 (see the end of the proof of prop 6.9 on page 119, for example). Now I know SGA 8 was never made, but I was wondering:

Does anyone have a good guess as to what this theorem should say?

Does anyone have a good reference for a quick and "hands off" introduction to descent theory? I am really just looking to understand the "gist" of it.

Technique de descente et théorèmes d'existence en géométrie algébrique, Parts I,II available on Numdam.org $\endgroup$ – Mahdi Majidi-Zolbanin Jan 7 '12 at 16:30