Foundations of Algebraic Geometry
!! TO-DO: translator’s note !!
explain which chapters correspond to which FGAs
mention bibliography numbering changes
In the Séminaire Bourbaki, between 1957 and 1962, we gave eight exposés on the foundations of algebraic geometry. With the exception of the first, these exposés are expressed in the language of schemes. All of the stated results will find their place in Jean Dieudonné and Alexander Grothendieck’s “Éléments de géométrie algébrique”. However, none of the essence of any of these exposés is currently found in any of the chapters (neither published nor still in preperation) of the EGA, nor in any other book or article, and this will probably remain the case for a few more years still. This is the main reason that persuaded us to combine these exposés, giving readers access to a number of ideas and key results of the theory of schemes whilst awaiting a well-written summary. Also, reading these chapters will allow the reader to quickly familiarise themselves with the aforementioned results and ideas, without being bothered by the necessarily cumbersome details of a systematic treatment, and also endow them with vital motivations for the study of such a treatment.
For the sake of the reader, we have assembled here some comments and errata, grouped by exposé, that, most notably, show the progress accomplished since the editing of this text, as well as indicating some supplementary references.1
Many of the results appearing in these exposés have been discussed in detail in the Séminaire de Géométrie Algébrique du Bois Marie, as well as in the two subsequent seminars at Harvard, in 1961–62 (the first by myself, and the second by Mumford–Tate), the notes for which are currently in preparation by Lichtenbaum.
[Trans.] Rather than translating the comments and errata here, we have inserted them throughout the text in the relevant places; we preface them with “[Comp.]” (except for small corrections, which we have inserted silently).↩︎