Introduction
Volume I — The Language of Schemes
1.
Front matter
2.
Chapter preliminaries
3.
Rings of fractions
4.
Irreducible and noetherian spaces
5.
Complements on sheaves
6.
Ringed spaces
7.
Quasi coherent and coherent sheaves
8.
Flatness
9.
Adic rings
10.
Chapter language of schemes
11.
Affine schemes
12.
Preschemes and morphisms
13.
Product of preschemes
14.
Subpreschemes and immersions
15.
Reduced preschemes and separation
16.
Finiteness conditions
17.
Rational maps
18.
Chevalley schemes
19.
Complements on quasi coherent sheaves
20.
Formal schemes
21.
Bibliography
22.
Translation glossary
23.
Index of notation
24.
Index of terminology
Volume II — Some Classes of Morphisms
25.
Front matter
26.
Affine morphisms
27.
Homogeneous prime spectra
28.
Homogeneous spectrum sheaf graded algebras
29.
Projective bundles ample sheaves
30.
Quasi affine quasi projective morphisms
31.
Integral finite morphisms
32.
Valuative criteria
33.
Blow ups projecting cones
34.
Bibliography
35.
Translation conventions
36.
Index of notations
37.
Index of terminology
38.
Translation ledger
Volume III — Cohomology of Coherent Sheaves
39.
Front matter (part 1)
40.
Front matter (part 2)
41.
Ch.0 §8. Representable functors
42.
Ch.0 §9. Constructible sets
43.
Ch.0 §10. Complements flat modules
44.
Ch.0 §11. Complements homological algebra
45.
Ch.0 §12. Complements cohomology sheaves
46.
Ch.0 §13. Projective limits homological algebra
47.
Ch.3 §0. Introduction
48.
Ch.3 §1. Cohomology affine schemes
49.
Ch.3 §2. Cohomology projective morphisms
50.
Ch.3 §3. Finiteness proper morphisms
51.
Ch.3 §4. Fundamental theorem proper morphisms
52.
Ch.3 §5. Existence coherent algebraic sheaves
53.
Ch.3 §6. Tor functors kunneth formula
54.
Ch.3 §7. Base change homological functors
55.
Bibliography
56.
Translation conventions
57.
Index of notations
58.
Index of terminology
59.
Translation ledger
Volume IV — Local Study of Schemes and Morphisms
60.
Front matter (part 1)
61.
Front matter (part 2)
62.
Front matter (part 3)
63.
Front matter (part 4)
64.
Ch.0 §14. Combinatorial dimension
65.
Ch.0 §15. Mf regular sequences
66.
Ch.0 §16. Dimension and depth
67.
Ch.0 §17. Regular rings
68.
Ch.0 §18. Extensions of algebras
69.
Ch.0 §19. Formally smooth algebras
70.
Ch.0 §20. Derivations and differentials
71.
Ch.0 §21. Differentials characteristic p
72.
Ch.0 §22. Differential criteria
73.
Ch.0 §23. Japanese rings
74.
Ch.4 §0. Introduction
75.
Ch.4 §1. Relative finiteness conditions
76.
Ch.4 §2. Base change and flatness
77.
Ch.4 §3. Associated prime cycles
78.
Ch.4 §4. Base field change
79.
Ch.4 §5. Dimension depth regularity
80.
Ch.4 §6. Flat morphisms
81.
Ch.4 §7. Noetherian completion
82.
Ch.4 §8. Projective limits
83.
Ch.4 §9. Constructible properties
84.
Ch.4 §10. Jacobson preschemes
85.
Ch.4 §11. Flatness loci and descent
86.
Ch.4 §12. Study of fibers
87.
Ch.4 §13. Equidimensional morphisms
88.
Ch.4 §14. Universally open morphisms
89.
Ch.4 §15. Fibers of a morphism
90.
Ch.4 §16. Differential invariants
91.
Ch.4 §17. Smooth unramified etale morphisms
92.
Ch.4 §18. Complements etale morphisms
93.
Ch.4 §19. Regular immersions
94.
Ch.4 §20. Meromorphic functions
95.
Ch.4 §21. Divisors
96.
Bibliography
97.
Translation conventions
98.
Index of notations
99.
Index of terminology
100.
Translation ledger
Volume V — Construction of Schemes (unpublished)
101.
Front matter
102.
Ch.5 §1. Singular supersingular sets
103.
Ch.5 §2. Jacobian supplements
104.
Ch.5 §5. Hyperplane sections part 1
105.
Ch.5 §5. Hyperplane sections part 2
106.
Ch.5 §6. Invertible sheaves and divisors
107.
Bibliography
108.
Translation conventions
109.
Index of notations
110.
Index of terminology
111.
Translation ledger
Light
Rust
Coal
Navy
Ayu
Éléments de Géométrie Algébrique — English
Chapter 0 — Preliminaries
§1. Rings of fractions
§2. Irreducible spaces. Noetherian spaces
§3. Complements on sheaves
§4. Ringed spaces
§5. Quasi-coherent sheaves and coherent sheaves
§6. Flatness
§7. Adic rings