Index of terminology

Alphabetized by the English head term. Section numbers refer to the defining occurrence; the chapter prefix ($0_{III}$, III) is included where ambiguous.

A

• Abutment of a spectral sequence: 0_III.11.1.1.
• Algebraizable (${\mathcal{O}}_X$-module): III.5.2.1.
• Algebraizable (formal scheme): III.5.4.2.
• Analytically integral (ring): III.4.3.6.
• Augmentation of a resolution: 0_III.11.4.1.

B

• Bi-alternating cochain: 0_III.11.8.4.
• Bicomplex: 0_III.11.2.1.

C

• Cartan–Eilenberg resolution (right, injective): 0_III.11.4.2.
• Cartan–Eilenberg resolution (left, projective): 0_III.11.6.1.
• Characteristic, Euler–Poincaré, of a complex: 0_III.11.10.1.
• Characteristic, Euler–Poincaré, of a coherent ${\mathcal{O}}_X$-module ($X$ projective over $\mathrm{Spec}(A)$, $A$ Artinian): III.2.5.1.
• Characteristic, Euler–Poincaré, of a complex of modules: III.7.9.5.
• Cohomologically flat (at a point, on $Y$, in dimension $p$): III.7.8.1.
• Complex defined by a bicomplex: 0_III.11.3.1.
• Complexes, homotopic: III.6.1.4.
• Condition (ML): 0_III.13.1.2.
• Condition (TF), condition (TN): see EGA II.
• Constructible (subset, set): 0_III.9.1.2.
• Constructible (function): 0_III.9.3.1.
• Cup product: 0_III.12.1.2.

D

• Dévissage lemma: III.3.1.2.
• Di-homomorphism (for algebraic structures on categories): 0_III.8.2.1.

E

• Edge homomorphism (of a spectral sequence): 0_III.12.2.4 (and elsewhere).
• Essentially constant (projective system): 0_III.13.4.2.
• Euler–Poincaré characteristic, see Characteristic.
• Exact (subset of an abelian category): III.3.1.1.

F

• Filtration, co-discrete: 0_III.11.1.3.
• Filtration, co-separated, discrete, exhaustive, finite, separated: 0_III.11.1.3.
• Filtration, $\mathfrak{J}$-good ($J$-good): 0_III.13.7.7.
• Final (object of a category): 0_III.8.1.10.
• Finite (morphism of formal preschemes): III.4.8.2.
• Finite (formal prescheme over $\mathfrak{D}$), $\mathfrak{D}$-finite (formal prescheme): III.4.8.2.
• Formal prescheme: see EGA I, Ch. I §10.
• Formula, Künneth: III.6.7.8.
• Functor, canonical covariant: 0_III.8.1.2.
• Functor, contravariant (covariant): 0_III.8.1.1.
• Functor, fully faithful: 0_III.8.1.5.
• Functor, representable: 0_III.8.1.8.
• Functorial morphism (modern: natural transformation): 0_III.8.1.2.
• Fundamental theorem (of proper morphisms): III.4.1.1.
• Fundamental theorem (of projective morphisms): III.2.2.1.

G

• Generization (of a point): 0_III.9.3.4.
• Genus, arithmetic: III.2.5.1.
• Geometrically connected (fiber): III.4.3.4.
• Graded object associated to a projective system satisfying (ML): 0_III.13.4.2.
• Graded object bounded below (above): 0_III.11.2.1.

H

• Hilbert polynomial: III.2.5.3.
• Hilbert polynomial relative to a complex of modules: III.7.9.12.
• Homologically flat (at a point, on $Y$, in dimension $p$): III.7.8.1.
• Homomorphism of algebraic structures on categories: 0_III.8.2.1.
• Homotopism: III.6.1.4.
• Hypercohomology of a functor relative to a complex $K^{\bullet }$: 0_III.11.4.3.
• Hypercohomology of a bifunctor relative to two complexes $K^{\bullet }$, $K^{\prime \bullet }$: 0_III.11.4.6.
• Hyperhomology of a functor relative to a complex $K_{\bullet }$: 0_III.11.6.2.
• Hyperhomology of a bifunctor relative to two complexes $K_{\bullet }$, $K_{\bullet }^{\prime }$: 0_III.11.6.6.
• Hyperhomology of a functor relative to a bicomplex: 0_III.11.7.2.
• Hypertor of two complexes of $A$-modules: III.6.3.1.
• Hypertor, local, of two complexes of modules: III.6.4.1.
• Hypertor, global, of two complexes of modules: III.6.6.2, III.6.6.8, III.6.7.3.

K

• Künneth formula: III.6.7.8.
• Künneth spectral sequences: III.6.7.3.

L

• Lemma, Chow's: III.3.2.1 (cited as the EGA II result).
• Lemma, dévissage: III.3.1.2.
• Limit, projective / inductive: 0_III.8.1.9 / 0_III.8.1.11.
• Locally constructible (set): 0_III.9.1.11.
• Loi de composition externe (interne) on the objects of a category: 0_III.8.2.1.

M

• Mittag–Leffler condition: see Condition (ML).
• Morphism, affine: see EGA II.
• Morphism, finite of formal preschemes: III.4.8.2.
• Morphism, proper of formal preschemes: III.3.4.1.
• Morphism, projective: see EGA II.
• Morphism, of spectral sequences: 0_III.11.1.2.
• Morphism, universally open: III.4.3.9.
• Morphism, functorial: 0_III.8.1.2.

N

• Norm, see EGA II.

O

• $\mathcal{C}$-object in groups: 0_III.8.2.3.
• $\mathcal{C}$-group, $\mathcal{C}$-ring, $\mathcal{C}$-module: 0_III.8.2.3.
• Object of boundaries, of coboundaries, of cycles, of cocycles: 0_III.11.2.1.
• Object of universal images: 0_III.13.1.1.
• Object, final, of a category: 0_III.8.1.10.
• Object, graded, associated to a projective system satisfying (ML): 0_III.13.4.2.

P

• Periodic (graded algebra): see EGA II.
• Polynomial, Hilbert: III.2.5.3.
• Polynomial, Hilbert relative to a complex of modules: III.7.9.12.
• Prescheme, see EGA I, EGA II.
• Prescheme, formal: see EGA I, Ch. I §10.
• Proper part (over $\mathfrak{D}$) of a formal prescheme: III.3.4.1.
• Proper (morphism of formal preschemes): III.3.4.1.

R

• Representable (functor): 0_III.8.1.8.
• Resolution, Cartan–Eilenberg, right, injective: 0_III.11.4.2.
• Resolution, Cartan–Eilenberg, left, projective: 0_III.11.6.1.
• Resolution, cohomological, right, left, homological, injective, free, flat, projective: 0_III.11.4.
• Retrocompact (set): 0_III.9.1.1.

S

• Sheaf of rings of cohomological dimension $\le n$: III.6.5.5.
• Space, ringed, of cohomological dimension $\le n$: III.6.5.5.
• Spectral sequence in an abelian category: 0_III.11.1.1.
• Spectral sequence, biregular: 0_III.11.1.3.
• Spectral sequence, coregular: 0_III.11.1.3.
• Spectral sequence, degenerate: 0_III.11.1.6.
• Spectral sequence, of a functor relative to a filtered object: 0_III.13.6.4.
• Spectral sequence, regular: 0_III.11.1.3.
• Spectral sequence, weakly convergent: 0_III.11.1.3.
• Spectral sequences, Künneth: III.6.7.3.
• Spectral sequences, of a bicomplex: 0_III.11.3.2 and 0_III.11.3.5.
• Spectral sequences, hypercohomology of a functor relative to a complex: 0_III.11.4.3.
• Spectral sequences, hyperhomology of a functor relative to a complex: 0_III.11.6.2.
• Spectral sequences, hyperhomology of a functor relative to a bicomplex: 0_III.11.7.2.
• Stein factorization: III.4.3.3.
• Strict (projective system): 0_III.13.4.2.
• Subcategory, full: 0_III.8.1.5.
• Subset, exact (in an abelian category): III.3.1.1.
• System of coefficients: 0_III.11.8.4.

T

• Theorem, finiteness for proper morphisms: III.3.2.1.
• Theorem, fundamental, of projective morphisms: III.2.2.1.
• Theorem, fundamental, of proper morphisms: III.4.1.1.
• Theorem, existence of coherent algebraic sheaves: III.5 (the main theorem).

U

• Unibranch (ring, point): III.4.3.6.
• Universally open morphism: III.4.3.9.