3094indexindex.xmlGrothendieck's "Foundations of Algebraic Geometry" (FGA)Click for PDF version2889translators-notetranslators-note.xmlNote from the translatorindexThis is an English translation of Alexander Grothendieck's "Fondements de la Géometrie Algébrique". The original (French) notes have been scanned and uploaded by the Grothendieck Circle here, though you can also find the individual talks, as well as the errata, on Numdam.The translator (Tim Hosgood) takes full responsibility for any errors introduced, and claims no rights to any of the mathematical content herein. Any notes by the translator are in italics and prefixed with "[Trans.]".You can view the entire source code of this translation (and contribute or submit corrections) in the GitHub repository. Corrections and comments welcome.The translator would like to sincerely thank Steve Hnizdur for catching many typos and mistakes, as well as Jon Sterling for helping with the technical support in getting this translation ported to run on Forester. Foreword Duality theorems for coherent algebraic sheaves Formal geometry and algebraic geometry Technique of descent and existence theorems in algebraic geometry Generalities, and descent by faithfully flat morphisms The existence theorem and the formal theory of modules Quotient preschemes Hilbert schemes Picard schemes: Existence theorems Picard schemes: General properties Bibliography