# 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)***Preliminaries (EGA 0_I)***(proofread by @thosgood)*- [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)*

- [x] 1. Rings of fractions
**Preliminaries (EGA 0_III)**- [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)

- [x] 8. Representable functors
**Preliminaries (EGA 0_IV)**- [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)

- [x] (14-ε). Summary
**The language of schemes (EGA I)***(proofread by @thosgood)*- [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)**- [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)*

- [x] 0. Summary
**Cohomological study of coherent sheaves (EGA III)**- [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)*

- [x] 0. Summary
**Local study of schemes and their morphisms (EGA IV)**- [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)*

- [x] 0. Summary