Éléments de Géométrie Algébrique — English Translation

This site is a complete English translation of EGA — the Éléments de Géométrie Algébrique by Alexander Grothendieck, written in collaboration with Jean Dieudonné (Publications mathématiques de l’IHÉS, 1960–1967). The EGA is the foundational treatise of modern scheme-theoretic algebraic geometry; this edition makes the full text, from EGA I through the unfinished EGA V, readable in English for the first time in a single, unified work.

The translation is idiomatic English with LaTeX mathematics, rendered as static, browser-readable HTML. It is LLM-generated (see Translation principles below) and openly licensed.

What distinguishes this edition

• Browser-readable HTML — no PDF viewer required; every page renders server-side, including the mathematics.
• Stable, direct section links — each section and paragraph of EGA has its own URL.
• Original numbering preserved — EGA’s decimal numbering $(N.M.K)$, $(0,N.M.K)$, $(I,N.M.K)$ is reproduced exactly, so citations of the French original resolve here unchanged.
• Original-page markers — transitions of the original Publ. Math. IHÉS pagination are marked inline.
• Glossaries and modern-terminology notes — each volume carries a translation glossary mapping Grothendieck’s historical terms (e.g. prescheme) to their modern equivalents.
• Hyperlinked cross-references — citations within EGA, and between EGA and the companion SGA English translation, are clickable links.

Volumes

• EGA I — The Language of Schemes (Le langage des schémas, 1960)
• EGA II — Elementary Global Study of Some Classes of Morphisms (Étude globale élémentaire de quelques classes de morphismes, 1961)
• EGA III — Cohomological Study of Coherent Sheaves (Étude cohomologique des faisceaux cohérents, 1961–1963)
• EGA IV — Local Study of Schemes and Morphisms of Schemes (Étude locale des schémas et des morphismes de schémas, 1964–1967)
• EGA V — Construction of Schemes (unpublished) — reconstructed material

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.