EGA

Community translation (French to English) of A. Grothendieck's EGA. S’il-vous plaît pardonnez-nous, Grothendieck.

To compile, make book, make pdfs, or make all.

PDFs

There is the full document, or individual sections can be downloaded separately:

• What this is.
• Introduction.
• EGA 0.
• EGA I.
• EGA II.
• EGA III.
• EGA IV.
• References.

All the PDFs are auto-compliled every hour if any changes have been made since the last auto-compile, so will always be up to date with the latest commit.

Current status

	First draft	Proofreading

Here is the current status of the translation, along with who is currently working on/has worked on which sections.

• Introduction (EGA I) (proofread by @thosgood)
• Preliminaries (EGA 0_I) (proofread by @thosgood)
  • 1. Rings of fractions (@ryankeleti)
  • 2. Irreducible spaces. Noetherian spaces (@ryankeleti)
  • 3. Supplement on sheaves (@ryankeleti)
  • 4. Ringed spaces (@ryankeleti)
  • 5. Quasi-coherent sheaves and coherent sheaves (@ryankeleti)
  • 6. Flatness (@ryankeleti)
  • 7. Adic rings (@ryankeleti)
• Preliminaries (EGA 0_III)
  • 8. Representable functors (@ryankeleti)
  • 9. Constructible sets (@ryankeleti)
  • 10. Supplement on flat modules (@thosgood)
  • 11. Supplement on homological algebra (@ryankeleti)
  • 12. Supplement on sheaf cohomology
  • 13. Projective limits in homological algebra
• Preliminaries (EGA 0_IV)
  • (14-ε). Summary (@thosgood)
  • 14. Combinatorial dimension of a topological space (@thosgood)
  • 15. M-regular and F-regular sequences
  • 16. Dimension and depth of Noetherian local rings
  • 17. Regular rings
  • 18. Supplement on extensions of algebras
  • 19. Formally smooth algebras and Cohen rings
  • 20. Derivations and differentials
  • 21. Differentials in rings of characteristic p
  • 22. Differential criteria for smoothness and regularity
  • 23. Japanese rings
• The language of schemes (EGA I) (proofread by @thosgood)
  • 0. Summary
  • 1. Affine schemes (@ryankeleti)
  • 2. Preschemes and their morphisms (@thosgood)
  • 3. Products of preschemes (@thosgood, @ryankeleti)
  • 4. Subpreschemes and immersions (@ryankeleti)
  • 5. Reduced preschemes; separation condition (@thosgood)
  • 6. Finiteness conditions (@thosgood)
  • 7. Rational maps (@thosgood)
  • 8. Chevalley schemes (@thosgood)
  • 9. Supplement on quasi-coherent sheaves (@thosgood)
  • 10. Formal schemes (@thosgood, @ryankeleti)
• Elementary global study of some classes of morphisms (EGA II)
  • 0. Summary (@ryankeleti / proofread by @thosgood)
  • 1. Affine morphisms (@ryankeleti)
  • 2. Homogeneous prime spectra
  • 3. Homogeneous prime spectrum of a sheaf of graded algebras
  • 4. Projective bundles; Ample sheaves
  • 5. Quasi-affine morphisms; quasi-projective morphisms; proper morphisms; projective morphisms (@thosgood)
  • 6. Integral morphisms and finite morphisms
  • 7. Valuative criteria
  • 8. Blowup schemes; based cones; projective closure (@thosgood)
• Cohomological study of coherent sheaves (EGA III)
  • 0. Summary (@thosgood / proofread by @thosgood)
  • 1. Cohomology of affine schemes (@ryankeleti)
  • 2. Cohomological study of projective morphisms
  • 3. Finiteness theorem for proper morphisms (@ryankeleti)
  • 4. The fundamental theorem of proper morphisms. Applications
  • 5. An existence theorem for coherent algebraic sheaves
  • 6. Local and global Tor functors; Künneth formula
  • 7. Base change for homological functors of sheaves of modules
  • 8. The duality theorem for projective bundles
  • 9. Relative cohomology and local cohomology; local duality
  • 10. Relations between projective cohomology and local cohomology. Formal completion technique along a divisor
  • 11. Global and local Picard groups
• Local study of schemes and their morphisms (EGA IV)
  • 0. Summary (@thosgood)
  • 1. Relative finiteness conditions. Constructible sets of preschemes
  • 2. Base change and flatness
  • 3. Associated prime cycles and primary decomposition
  • 4. Change of base field for algebraic preschemes
  • 5. Dimension, depth, and regularity of locally Noetherian preschemes
  • 6. Flat morphisms of locally Noetherian preschemes
  • 7. Relations between a local Noetherian ring and its completion. Excellent rings
  • 8. Projective limits of preschemes
  • 9. Constructible properties
  • 10. Jacobson preschemes
  • 11. Topological properties of finitely presented flat morphisms. Flatness criteria
  • 12. Fibres of finitely presented flat morphisms
  • 13. Equidimensional morphisms
  • 14. Universally open morphisms
  • 15. Fibres of a universally open morphism
  • 16. Differential invariants. Differentially smooth morphisms
  • 17. Smooth morphisms, unramified morphisms, and étale morphisms
  • 18. Supplement on étale morphisms. Henselian local rings and strictly local rings
  • 19. Regular immersions and normal flatness
  • 20. Meromorphic functions and pseudo-morphisms
  • 21. Divisors