Éléments de géométrie algébrique

The Éléments de géométrie algébrique ( "Elements of algebraic geometry ", short EGA ) by Alexander Grothendieck ( with the help of Jean Dieudonné ) are a 1.500seitige unfinished treatise on algebraic geometry, in eight parts ( fascicles ) gradually between 1960 and was published in 1967. Grothendieck tried systematically to rewrite the algebraic geometry by, overthrew the then common method of moving from one variety to a ring, and a ring constructed a variety. This is the basic idea for the construction of the so-called schemes.

Summary of chapters published:

• I. Le langage of schémas ( "The language of the schemas ").
• II Étude de quelques global élémentaire classes de morphismes ( " Global properties of some classes of morphisms ").
• III. Étude cohomologique of Faisceaux Coherent ( "the study of the cohomology of coherent sheaves ").
• IV Étude locale of schémas et des morphismes de schémas ( " Local properties of schemes and Schemamorphismen ").

In the beginning, 13 chapters planned (as in Euclid's Elements, which also contained 13 chapters, and a basic structure for the mathematics per se were ).