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.

  ISBN:978-0-8218-4245-4, MR2007f:14001

  lecture notes

Contents

See the conference page for scans of the lecture notes.

On stacks in the guise of fibered categories satisfying descent:

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

On Hilbert schemes:

• Nitin Nitsure, Construction of Hilbert and Quot schemes (105–137)

  MR2223407; math/0504590

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

On Picard schemes:

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

See also:

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

category: reference