Éléments de Géométrie Algébrique — English

An idiomatic, LLM-generated English translation (Markdown, LaTeX mathematics) of Grothendieck and Dieudonné's Éléments de Géométrie Algébrique (Publications mathématiques de l'IHÉS, 1960–1967).

Volumes

• Volume I — The Language of Schemes
• Volume II — Some Classes of Morphisms
• Volume III — Cohomology of Coherent Sheaves
• Volume IV — Local Study of Schemes and Morphisms
• Volume V — Construction of Schemes (unpublished)

Translation principles

• Preserve EGA's historical terminology (notably prescheme / scheme); inline the modern gloss on first occurrence per section, and keep a per-volume translation glossary.
• Preserve EGA's decimal numbering exactly: $(N.M.K)$ within a chapter, $(0,N.M.K)$ for Chapter 0 references, $(I,N.M.K)$ for cross-chapter references.
• Mark original page transitions inline as HTML comments (<!-- original page n -->).
• Revise prose for English mathematical idiom while preserving Grothendieck's architectural voice.

Source

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.

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.