The Éléments de géométrie algébrique ("Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné), or EGA for short, are an unfinished 1500-page treatise, in French, on algebraic geometry that was published (in eight parts or fascicules) from 1960 through 1967 by the Institut des Hautes Études Scientifiques. In it, Grothendieck attempted to establish systematic foundations of algebraic geometry, building upon the concept of schemes, which he defined. The work is now considered the founding stone and basic reference of all modern algebraic geometry.
The table of contents is as follows:
- I. Le langage des schémas ("The language of schemes").
- II. Étude globale élémentaire de quelques classes de morphismes ("Global elementary study of certain classes of morphisms").
- III. Étude cohomologique des faisceaux cohérents ("Cohomological study of coherent sheaves").
- IV. Étude locale des schémas et des morphismes de schémas ("Local study of schemes and morphisms of schemes").
Initially thirteen sections were planned. Some of the material which would have been found in the following sections can be found, in a less perfected form, in the Séminaire de géométrie algébrique.
A scanned copy of the EGA can be found at the NUMDAM archive, under "Publications mathématiques de l'IHÉS" (volumes 4, 8, 11, 17, 20, 24, 28 and 32).
