Elements of algebraic geometry

See also: EGA

The Elements of algebraic geometry of Alexander Grothendieck (helped by Jean Dieudonné), or EGA in summary, are an unfinished treaty of 1500 pages, in French, on the algebraic Géométrie which was published (in eight parts or booklets) between 1960 and 1967 by the Institut of the High Scientific studies. Grothendieck tries there to establish the bases of the algebraic geometry systematically, and built there the concept of the diagrams, which it defines. This work is nowadays regarded as the first stone and the basic reference of the modern algebraic geometry.

Contents

  • I. the language of the diagrams.
  • II. Elementary general study of some classes of morphisms.
  • III. Cohomologic study of the coherent beams.
  • IV. Local study of the diagrams and the morphisms of diagrams.

Initially, thirteen chapters were laid down. Some of the results which one could have found in the following chapters find, in a less completed form, in the algebraic Séminaire of geometry. An outline of the chapter V was translated into English, cf.

Published in the “mathematical Publications of the IHÉS” (vol. 4,8,11,17,20,24,28 and 32). the EGA were digitized within the framework of the program NUMDAM NUMDAM.

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