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EGA

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

View online here.

For discussion regarding this project, visit #ega:matrix.org!

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

PDFs

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

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

Here is the current status of the translation, along with who is currently working on/has worked on which sections. (Page counts and percentages are usually just rough estimates).

  • Introduction (EGA I) (proofread by @thosgood) introstatus
  • Preliminaries (EGA 0_I) (proofread by @thosgood) EGA0(I)status
    • [x] 1. Rings of fractions (@ryankeleti)
    • [x] 2. Irreducible spaces. Noetherian spaces (@ryankeleti)
    • [x] 3. Supplement on sheaves (@ryankeleti)
    • [x] 4. Ringed spaces (@ryankeleti)
    • [x] 5. Quasi-coherent sheaves and coherent sheaves (@ryankeleti)
    • [x] 6. Flatness (@ryankeleti)
    • [x] 7. Adic rings (@ryankeleti)
  • Preliminaries (EGA 0_III) EGA0(III)status
    • [x] 8. Representable functors (@ryankeleti)
    • [x] 9. Constructible sets (@ryankeleti)
    • [x] 10. Supplement on flat modules (@thosgood)
    • [ ] 11. Supplement on homological algebra (@ryankeleti)
    • [ ] 12. Supplement on sheaf cohomology (~25 pages)
    • [ ] 13. Projective limits in homological algebra (~10 pages)
  • Preliminaries (EGA 0_IV) EGA0(IV)status
    • [x] (14-ε). Summary (@thosgood)
    • [x] 14. Combinatorial dimension of a topological space (@thosgood)
    • [ ] 15. M-regular and F-regular sequences (~10 pages)
    • [ ] 16. Dimension and depth of Noetherian local rings (~15 pages)
    • [ ] 17. Regular rings (~15 pages)
    • [ ] 18. Supplement on extensions of algebras (~20 pages)
    • [ ] 19. Formally smooth algebras and Cohen rings (~45 pages)
    • [ ] 20. Derivations and differentials (~35 pages)
    • [ ] 21. Differentials in rings of characteristic p (~30 pages)
    • [ ] 22. Differential criteria for smoothness and regularity (~30 pages)
    • [ ] 23. Japanese rings (~5 pages)
  • The language of schemes (EGA I) (proofread by @thosgood) EGAIstatus
    • [x] 0. Summary
    • [x] 1. Affine schemes (@ryankeleti)
    • [x] 2. Preschemes and their morphisms (@thosgood)
    • [x] 3. Products of preschemes (@thosgood, @ryankeleti)
    • [x] 4. Subpreschemes and immersions (@ryankeleti)
    • [x] 5. Reduced preschemes; separation condition (@thosgood)
    • [x] 6. Finiteness conditions (@thosgood)
    • [x] 7. Rational maps (@thosgood)
    • [x] 8. Chevalley schemes (@thosgood)
    • [x] 9. Supplement on quasi-coherent sheaves (@thosgood)
    • [x] 10. Formal schemes (@thosgood, @ryankeleti)
  • Elementary global study of some classes of morphisms (EGA II) EGAIIstatus
    • [x] 0. Summary (@ryankeleti / proofread by @thosgood)
    • [x] 1. Affine morphisms (@ryankeleti)
    • [ ] 2. Homogeneous prime spectra (~30 pages) (@thosgood)
    • [ ] 3. Homogeneous prime spectrum of a sheaf of graded algebras (~20 pages)
    • [x] 4. Projective bundles; Ample sheaves (@thosgood)
    • [x] 5. Quasi-affine morphisms; quasi-projective morphisms; proper morphisms; projective morphisms (@thosgood)
    • [ ] 6. Integral morphisms and finite morphisms (~25 pages)
    • [x] 7. Valuative criteria (@thosgood)
    • [x] 8. Blowup schemes; based cones; projective closure (@thosgood)
    • [x] Errata and addenda (list 1)
  • Cohomological study of coherent sheaves (EGA III) EGAIIIstatus
    • [x] 0. Summary (@thosgood / proofread by @thosgood)
    • [x] 1. Cohomology of affine schemes (@ryankeleti)
    • [ ] 2. Cohomological study of projective morphisms (~15 pages)
    • [x] 3. Finiteness theorem for proper morphisms (@ryankeleti)
    • [ ] 4. The fundamental theorem of proper morphisms. Applications (~30 pages)
    • [ ] 5. An existence theorem for coherent algebraic sheaves (~10 pages)
    • [ ] 6. Local and global Tor functors; Künneth formula (~40 pages)
    • [ ] 7. Base change for homological functors of sheaves of modules (~30 pages)
    • [x] 8. ~~The duality theorem for projective bundles~~
    • [x] 9. ~~Relative cohomology and local cohomology; local duality~~
    • [x] 10. ~~Relations between projective cohomology and local cohomology. Formal completion technique along a divisor~~
    • [x] 11. ~~Global and local Picard groups~~
    • [ ] Errata and addenda (list 2)
  • Local study of schemes and their morphisms (EGA IV) EGAIVstatus
    • [x] 0. Summary (@thosgood)
    • [ ] 1. Relative finiteness conditions. Constructible sets of preschemes (~30 pages)
    • [ ] 2. Base change and flatness (~30 pages)
    • [ ] 3. Associated prime cycles and primary decomposition (~15 pages)
    • [ ] 4. Change of base field for algebraic preschemes (~35 pages)
    • [ ] 5. Dimension, depth, and regularity of locally Noetherian preschemes (~50 pages)
    • [ ] 6. Flat morphisms of locally Noetherian preschemes (~50 pages)
    • [ ] 7. Relations between a local Noetherian ring and its completion. Excellent rings (~40 pages)
    • [ ] 8. Projective limits of preschemes (~50 pages)
    • [ ] 9. Constructible properties (~40 pages)
    • [ ] 10. Jacobson preschemes (~20 pages)
    • [ ] 11. Topological properties of finitely presented flat morphisms. Flatness criteria (~60 pages)
    • [ ] 12. Fibres of finitely presented flat morphisms (~15 pages)
    • [ ] 13. Equidimensional morphisms (~15 pages)
    • [ ] 14. Universally open morphisms (~25 pages)
    • [ ] 15. Fibres of a universally open morphism (~25 pages)
    • [x] 16. Differential invariants. Differentially smooth morphisms (@solov-t) (~50 pages)
    • [ ] 17. Smooth morphisms, unramified morphisms, and étale morphisms (@tholzschuh) (~55 pages)
    • [ ] 18. Supplement on étale morphisms. Henselian local rings and strictly local rings (~75 pages)
    • [ ] 19. Regular immersions and normal flatness (~40 pages)
    • [ ] 20. Meromorphic functions and pseudo-morphisms (~30 pages)
    • [ ] 21. Divisors (~75 pages)
    • [ ] Errata and addenda (list 3)