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EGA

Community translation (French to English) of A. Grothendieck's EGA. On est désolé, Grothendieck.

View online here. (the web version is not currently kept up to date; please refer to the PDF versions linked below)

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

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

PDFs

Individual volumes can be downloaded separately:

Alternatively, the full document can be downloaded:

(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

  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) EGA0(III)status

  • 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 (~25 pages)
  • 13. Projective limits in homological algebra (~10 pages)

Preliminaries (EGA 0_IV) EGA0(IV)status

  • (14-ε). Summary (@thosgood)
  • 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

  1. Summary
  2. Affine schemes (@ryankeleti)
  3. Preschemes and their morphisms (@thosgood)
  4. Products of preschemes (@thosgood, @ryankeleti)
  5. Subpreschemes and immersions (@ryankeleti)
  6. Reduced preschemes; separation condition (@thosgood)
  7. Finiteness conditions (@thosgood)
  8. Rational maps (@thosgood)
  9. Chevalley schemes (@thosgood)
  10. Supplement on quasi-coherent sheaves (@thosgood)
  11. Formal schemes (@thosgood, @ryankeleti)

Elementary global study of some classes of morphisms (EGA II) EGAIIstatus

  • 0. Summary (@ryankeleti / proofread by @thosgood)
  • 1. Affine morphisms (@ryankeleti)
  • 2. Homogeneous prime spectra (@thosgood)
  • 3. Homogeneous prime spectrum of a sheaf of graded algebras (~20 pages) (@thosgood)
  • 4. Projective bundles; Ample sheaves (@thosgood)
  • 5. Quasi-affine morphisms; quasi-projective morphisms; proper morphisms; projective morphisms (@thosgood)
  • 6. Integral morphisms and finite morphisms (~25 pages)
  • 7. Valuative criteria (@thosgood)
  • 8. Blowup schemes; based cones; projective closure (@thosgood)
  • Errata and addenda (list 1)

Cohomological study of coherent sheaves (EGA III) EGAIIIstatus

  • 0. Summary (@thosgood / proofread by @thosgood)
  • 1. Cohomology of affine schemes (@ryankeleti)
  • 2. Cohomological study of projective morphisms (~15 pages)
  • 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)
  • 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
  • Errata and addenda (list 2)

Local study of schemes and their morphisms (EGA IV) EGAIVstatus

  • 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)
  • 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)

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amateur translation project of Grothendieck's EGA.

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