nLab
EGA

Grothendieck among his many works published three series of works attempting to build the foundations for algebraic geometry.

  • The first is the series FGA written alone at the end of the 1950s; it is sort of quick outline of the theory and some deep results with proofs at the beginning of the period of the development of scheme theory?. A modern version of the material in FGA appeared as a book FGA explained (ICTP, Trieste 2003–2005).

  • EGA, written with help of Jean Dieudonné. This is a detailed work on scheme theory (our schemes are in EGA called preschemes; EGA’s schemes are what we call separated schemes). The numbering is nontrivial as it has chapter 0, the preliminaries, which were written at the beginning of various chapters. The published part of EGA is in Publ. IHÉS, now free online at numdam (detailed links to chapters will be added here later). We plan to list here the grand plan and some remarks and links. The thing is complicated by the existence of somewhat different reedition of EGA I as a single book 1971, which complicated citations.

  • SGA consists of the writeups of seminars at IHÉS lead by Grothendieck; the work of the members of the seminar under the guidance of Grothendieck are included. In nlab we keep entries SGA1, SGA4.

Both EGA and SGA were never completed. Part of the non-completed EGA existed as Grothendieck’s “prenotes”, and a small part of them has been preserved and a little piece even published. Part of the unfinished plan of SGA was attained in quick way by Pierre Deligne as SGA 412 (in other to justify preliminaries for his proof of the Weil conjecture?s), which Grothendieck did not approve.

See also Murfet’s summary notes for various parts of EGA.

category: reference