Fondements de la Géometrie Algébrique
Encyclopedia
FGA, or Fondements de la Géometrie Algébrique, is a book that collected together seminar notes of Alexander Grothendieck
. It is an
important source for his pioneering work on scheme theory, which laid foundations for algebraic geometry
in its modern technical developments.
The title is a translation of the title of Weil's book Foundations of algebraic geometry
.
It contained material on descent theory, and existence theorems including that for the Hilbert scheme
. The Technique de descente et théorèmes d'existence en géometrie algébrique is one series of seminars within FGA.
Like the bulk of Grothendieck's work of the IHÉS period, duplicated notes were circulated, but the publication was not as a conventional book.
Alexander Grothendieck
Alexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...
. It is an
important source for his pioneering work on scheme theory, which laid foundations for algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
in its modern technical developments.
The title is a translation of the title of Weil's book Foundations of algebraic geometry
Foundations of algebraic geometry
Foundations of algebraic geometry is a book by that develops algebraic geometry over fields of any characteristic. In particular it gives a careful treatment of intersection theory by defining the local intersection multiplicity of two subvarieties....
.
It contained material on descent theory, and existence theorems including that for the Hilbert scheme
Hilbert scheme
In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space , refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials...
. The Technique de descente et théorèmes d'existence en géometrie algébrique is one series of seminars within FGA.
Like the bulk of Grothendieck's work of the IHÉS period, duplicated notes were circulated, but the publication was not as a conventional book.
Contents
These are Séminaire Bourbaki notes, by number, from the years 1957 to 1962.- Fondements de la géométrie algébrique. Commentaires [Séminaire Bourbaki, t. 14, 1961/62, Complément];
- Théorème de dualité pour les faisceaux algébriques cohérents [Séminaire Bourbaki, t. 9, 1956/57, no. 149]; (coherent dualityCoherent dualityIn mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory....
) - Géométrie formelle et géométrie algébrique [Séminaire Bourbaki, t. 11, 1958/59, no. 182]; (formal geometry)
- Technique de descente et théorèmes d'existence en géométrie algébrique. I-VI
- I. Généralités. Descente par morphismes fidèlement plats [Séminaire Bourbaki, t. 12, 1959/60, no. 190];
- II. Le théorème d'existence en théorie formelle des modules [Séminaire Bourbaki, t. 12, 1959/60, no. 195];
- III. Préschémas quotients [Séminaire Bourbaki, t. 13, 1960/61, no. 212];
- IV. Les schémas de Hilbert [Séminaire Bourbaki, t. 13, 1960/61, no. 221];
- V. Les schémas de Picard. Théorèmes d'existence [Séminaire Bourbaki, t. 14, 1961/62, no. 232];
- VI. Les schémas de Picard. Propriétés générales [Séminaire Bourbaki, t. 14, 1961/62, no. 236]
See also
- Éléments de géométrie algébriqueÉléments de géométrie algébriqueThe Éléments de géométrie algébrique by Alexander Grothendieck , or EGA for short, is a rigorous treatise, in French, on algebraic geometry that was published from 1960 through 1967 by the Institut des Hautes Études Scientifiques...
- Grothendieck's Séminaire de géométrie algébriqueGrothendieck's Séminaire de géométrie algébriqueIn mathematics, the Séminaire de Géométrie Algébrique du Bois Marie was an influential seminar run by Alexander Grothendieck. It was a unique phenomenon of research and publication outside of the main mathematical journals that ran from 1960 to 1969 at the IHÉS near Paris...