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Fondements de la Géometrie Algébrique
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.
==Contents==
These are Séminaire Bourbaki notes, by number, from the years 1957 to 1962.
*(Fondements de la géométrie algébrique. Commentaires ) (Bourbaki, t. 14, 1961/62, Complément );
*(Théorème de dualité pour les faisceaux algébriques cohérents ) (Bourbaki, t. 9, 1956/57, no. 149 ); (coherent duality)
*(Géométrie formelle et géométrie algébrique ) (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 ) (Bourbaki, t. 12, 1959/60, no. 190 );
*
*(II. Le théorème d'existence en théorie formelle des modules ) (Bourbaki, t. 12, 1959/60, no. 195 );
*
*(III. Préschémas quotients ) (Bourbaki, t. 13, 1960/61, no. 212 );
*
*(IV. Les schémas de Hilbert ) (Bourbaki, t. 13, 1960/61, no. 221 );
*
*(V. Les schémas de Picard. Théorèmes d'existence ) (Bourbaki, t. 14, 1961/62, no. 232 );
*
*(VI. Les schémas de Picard. Propriétés générales ) (Bourbaki, t. 14, 1961/62, no. 236 )
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