nLab
FGA explained

One of the series of Grothendieck’s works is FGA (see entry EGA for overall description of EGA, FGA and SGA). A summer school in Trieste 2003, has tried to summarize some of the main historical breakthroughs of FGA in modern exposition. The proceedings of that school are an updated version of freely available materials on the ICTP web.

• Barbara Fantechi, Lothar Göttsche, Luc Illusie, Steven L. Kleiman, Nitin Nitsure, Angelo Vistoli, Fundamental algebraic geometry. Grothendieck’s FGA explained, Mathematical Surveys and Monographs 123, Amer. Math. Soc. 2005. x+339 pp. MR2007f:14001

Contents

• Angelo Vistoli, Grothendieck topologies, fibered categories and descent theory (1–104) MR2223406; math.AG/0412512.

• Nitin Nitsure, Construction of Hilbert and Quot schemes (105–137) MR2223407; (draft pdf)

• Barbara Fantechi and Lothar Göttsche, Local properties and Hilbert schemes of points (139–178) MR2223408; (draft pdf)

• Luc Illusie, Grothendieck's existence theorem in formal geometry (179–233) MR2223409; (draft version pdf)

• Steven L. Kleiman, The Picard scheme (235–321) MR2223410 (draft pdf)