# 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:

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)
- 1. Rings of fractions
*(@ryankeleti / proofread by @thosgood)* - 2. Irreducible spaces. Noetherian spaces
*(@ryankeleti / proofread by @thosgood)* - 3. Supplement on sheaves
*(@ryankeleti)* - 4. Ringed spaces
*(@ryankeleti)* - 5. Quasi-coherent sheaves and coherent sheaves
*(@ryankeleti)* - 6. Flatness
*(@ryankeleti)* - 7. Adic rings
*(@ryankeleti)*

- 1. Rings of fractions
- 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

- 8. Representable functors
- 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

- (14-ε). Summary
- The language of schemes (EGA I)
- 0. Summary
*(proofread by @thosgood)* - 1. Affine schemes
*(@ryankeleti / proofread by @thosgood)* - 2. Preschemes and their morphisms
*(@thosgood / proofread by @thosgood)* - 3. Products of preschemes
*(@thosgood, @ryankeleti / proofread by @thosgood)* - 4. Subpreschemes and immersions
*(@ryankeleti / proofread by @thosgood)* - 5. Reduced preschemes; separation condition
*(@thosgood / proofread by @thosgood)* - 6. Finiteness conditions
*(@thosgood)* - 7. Rational maps
*(@thosgood / proofread by @thosgood)* - 8. Chevalley schemes
*(@thosgood / proofread by @thosgood)* - 9. Supplement on quasi-coherent sheaves
*(@thosgood / proofread by @thosgood)* - 10. Formal schemes
*(@thosgood, @ryankeleti)*

- 0. Summary
- 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; projective cones; projective closure

- 0. Summary
- 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
- 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~~

- 0. Summary
- 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

- 0. Summary