''Fondements de la Géometrie Algébrique'' (''FGA'') is a book that collected together seminar notes of
Alexander Grothendieck
Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research ext ...
. It is an
important source for his pioneering work on
scheme theory
In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations and define the same algebraic variety but different s ...
, which laid foundations for
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
in its modern technical developments.
The title is a translation of the title of
André Weil
André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was one of the most influential mathematicians of the twentieth century. His influence is du ...
's book ''
Foundations of Algebraic Geometry
''Foundations of Algebraic Geometry'' is a book by that develops algebraic geometry over field (mathematics), fields of any characteristic (algebra), characteristic. In particular it gives a careful treatment of intersection theory by defining th ...
.''
It contained material on
descent theory, and existence theorems including that for the
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 (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a ...
. 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 éminaire Bourbaki, t. 14, 1961/62, ComplémentThéorème de dualité pour les faisceaux algébriques cohérents éminaire Bourbaki, t. 9, 1956/57, no. 149 (
coherent duality)
Géométrie formelle et géométrie algébrique éminaire 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 éminaire Bourbaki, t. 12, 1959/60, no. 190
II. Le théorème d'existence en théorie formelle des modules éminaire Bourbaki, t. 12, 1959/60, no. 195
III. Préschémas quotients éminaire Bourbaki, t. 13, 1960/61, no. 212
IV. Les schémas de Hilbert éminaire Bourbaki, t. 13, 1960/61, no. 221
V. Les schémas de Picard. Théorèmes d'existence éminaire Bourbaki, t. 14, 1961/62, no. 232
VI. Les schémas de Picard. Propriétés générales éminaire Bourbaki, t. 14, 1961/62, no. 236
See also
* ''
Éléments de géométrie algébrique
The (''EGA''; from French: "Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné) is a rigorous treatise on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the . ...
''
* ''
Séminaire de Géométrie Algébrique du Bois Marie''
References
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SGA, EGA, FGABy Mateo Carmona
{{DEFAULTSORT:Fondements de la Geometrie Algebrique
Algebraic geometry
1962 non-fiction books
Mathematics books