Séminaire de Géométrie Algébrique du Bois-Marie — English

An English translation of the SGA — the Séminaire de Géométrie Algébrique du Bois-Marie, the seminar directed by Alexander Grothendieck at the IHÉS in the 1960s that rebuilt the foundations of algebraic geometry. This edition presents the seminar volumes in idiomatic English (Markdown source, typeset mathematics), openly readable online. The translation is LLM-generated and edited for mathematical accuracy; the original French texts and their numbering are preserved throughout.

What distinguishes this edition

• Browser-readable and searchable HTML — no PDF required; the full text is indexed by the built-in site search.
• Directly linkable exposés and sections — every exposé is its own page, with stable URLs for citation.
• Original numbering preserved — exposés, sections, and statement numbers match the published French editions.
• Hyperlinked cross-references — citations to EGA are linked to the companion EGA English translation, and cross-references between SGA exposés are linked.
• Original-page markers — transitions of the original printed pages are marked inline.
• Terminology notes — each volume closes with a translation glossary and indexes of notations and terminology.

Volumes

• SGA 1 — Étale Coverings and the Fundamental Group (Grothendieck, with M. Raynaud; étale morphisms, descent, the étale fundamental group)
• SGA 2 — Local Cohomology and Lefschetz Theorems (Grothendieck; local cohomology, depth, duality, Lefschetz-type theorems)
• SGA 3 — Group Schemes (Demazure–Grothendieck; group schemes, multiplicative-type groups, reductive groups)
• SGA 4 — Topoi and Sites (Artin–Grothendieck–Verdier; presheaves, topologies, sheaves, topoi — in progress)

Translation principles

• Preserve the original numbering of Exposés, sections, and statements.
• Keep technical terms close to community-standard English (étale, scheme, descent); inline a brief definition the first time a term appears in an exposé.
• Mark original page transitions inline as HTML comments where helpful.
• Revise prose for English mathematical idiom while preserving the seminar voice of the originals.

Sources

The French source text was drawn from the Grothendieck Circle’s archive of Grothendieck’s published writings: https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/pubtexts.php. LaTeX community editions (where they exist) were cross-referenced for technical accuracy.

License

The translation is © 2026 Jacob Reinhold and licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). The underlying French text remains © the original authors and publishers.