EGA
Community translation (French to English) of A. Grothendieck and J. Dieudonné's Éléments de géométrie algébrique.
Désolé, Grothendieck.
For discussion regarding this project, visit #ega:matrix.org!
To compile, make book
, make pdfs
, or make all
.
PDFs
The PDFs are automatically generated whenever any changes are made, and you can always find the latest version on the releases page.
Current status
Summary:
- [x] EGA I preliminaries
- [x] EGA I
- [x] EGA II
- [ ] EGA III preliminaries
- [ ] EGA III
- [ ] EGA IV preliminaries
- [ ] EGA IV
Details:
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 0I) (proofread by @thosgood)_
- Rings of fractions (@ryankeleti)
- Irreducible spaces. Noetherian spaces (@ryankeleti)
- Supplement on sheaves (@ryankeleti)
- Ringed spaces (@ryankeleti)
- Quasi-coherent sheaves and coherent sheaves (@ryankeleti)
- Flatness (@ryankeleti)
- Adic rings (@ryankeleti)
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, @wayneyang108)
- [ ] 12. Supplement on sheaf cohomology (~25 pages)
- [ ] 13. Projective limits in homological algebra (~10 pages)
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)
The language of schemes (EGA I) (proofread by @thosgood)
- Summary
- Affine schemes (@ryankeleti)
- Preschemes and their morphisms (@thosgood)
- Products of preschemes (@thosgood, @ryankeleti)
- Subpreschemes and immersions (@ryankeleti)
- Reduced preschemes; separation condition (@thosgood)
- Finiteness conditions (@thosgood)
- Rational maps (@thosgood)
- Chevalley schemes (@thosgood)
- Supplement on quasi-coherent sheaves (@thosgood)
- 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)
- [x] 2. Homogeneous prime spectra (@thosgood)
- [x] 3. Homogeneous prime spectrum of a sheaf of graded algebras (@thosgood)
- [x] 4. Projective bundles; Ample sheaves (@thosgood)
- [x] 5. Quasi-affine morphisms; quasi-projective morphisms; proper morphisms; projective morphisms (@thosgood)
- [x] 6. Integral morphisms and finite morphisms (@thosgood)
- [x] 7. Valuative criteria (@thosgood)
- [x] 8. Blowup schemes; based cones; projective closure (@thosgood)
- [x] Errata and addenda (list 1) (@thosgood)
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) (@thosgood)
- [x] 3. Finiteness theorem for proper morphisms (@ryankeleti)
- [ ] 4. The fundamental theorem of proper morphisms. Applications (~30 pages) (@calebji0)
- [ ] 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)
- [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)
To-do (incomplete)
- check errata in EGA III and onwards
- more consistent use of Proposition/Theorem/Definition/whatever in front of
\sref
s
- lists of notation?
- terminology indices?
- hyperref links to equations (e.g. 3.3.9.1)
- check for any
\unsure
commands in the source
- check that all
\hyperref
references are found
- when this is finished (?!) should we assign a DOI?
- web version? (work in progress!)
- more detailed style guidelines? (e.g. language, sentence construction, etc.)
- link (M), (G), (T) references