Index of terminology

Alphabetized by the English head term. Section numbers refer to the defining occurrence in EGA II (without volume prefix); for cross-volume references, see the prose of each section.

A

• Affine cone defined by a graded ${\mathcal{O}}_Y$-algebra: 8.3.1.
• Affine morphism: 1.6.1.
• Affine prescheme over a prescheme: 1.2.1.
• Algebraic curve over a field: 7.4.2.
• Algebraic curve, complete: 7.4.7.
• Ample (invertible $\mathcal{O}$-module): 4.5.3.
• Ample, relative to $f$ ($f$-ample, $Y$-ample) (invertible $\mathcal{O}$-module): 4.6.1.
• Apex prescheme of an affine (projective) cone: 8.3.3.
• Apex section of an affine (projective) cone: 8.3.3.
• Associated to an ${\mathcal{O}}_S$-algebra ($S$-scheme): 1.3.1.
• Associated to an ${\mathcal{O}}_X$-module (sheaf): 1.4.3.
• Associated to a graded $S$-module (sheaf): 2.5.3.
• Associated to a graded $\mathcal{S}$-module (sheaf): 3.2.2.

B

• Blow-up prescheme: 8.1.3.

C

• Canonical morphism $G(\mathcal{E})\to \mathrm{Proj}(S)$ ($S={\oplus }_{n\ge 0}\Gamma (X,\mathcal{S}{\otimes }^n)$): 4.5.1.
• Canonical morphism $X\to \mathrm{Spec}(\Gamma (X,{\mathcal{O}}_X))$: 5.1.1.
• Canonical retraction of a punctured projective cone onto its locus at infinity: 8.3.5.
• Canonical section of ${\mathcal{O}}_X(-1)$ ($X$ a blow-up prescheme): 8.1.9.
• Characteristic polynomial of an endomorphism of a finite-type module over an integral ring: 6.4.2.
• Characteristic polynomial of an endomorphism of a finite-type module over a reduced Noetherian ring: 6.4.7.
• Chow’s lemma: 5.6.1.
• Complete algebraic curve: 7.4.7.
• Condition (TF), condition (TN): 2.7.2; 3.4.2.
• Cone, affine; cone, projective, defined by a graded ${\mathcal{O}}_Y$-algebra: 8.3.1.
• Cone, punctured affine; cone, punctured projective, defined by a graded ${\mathcal{O}}_Y$-algebra: 8.3.4.

D

• Determinant of an endomorphism of a finite-type module over an integral ring: 6.4.2.
• Determinant of an endomorphism of a finite-type module over a reduced Noetherian ring: 6.4.7.
• Determinant of an endomorphism of a locally free $\mathcal{A}$-module: 6.4.8.
• Determinant of an endomorphism of a finite-type ${\mathcal{O}}_X$-module over a locally integral prescheme $X$: 6.4.9.
• Determinant of an endomorphism of a finite-type ${\mathcal{O}}_X$-module over a locally Noetherian, reduced prescheme $X$: 6.4.10.

E

• Elementary symmetric functions of an endomorphism of a locally free module: 6.4.1.
• Elementary symmetric functions of an endomorphism of a finite-type module over an integral ring: 6.4.2.
• Elementary symmetric functions of an endomorphism of a finite-type module over a reduced Noetherian ring: 6.4.7.
• Elementary symmetric functions of an endomorphism of a locally free $\mathcal{A}$-module of constant rank: 6.4.8.
• Elementary symmetric functions of an endomorphism of a finite-type ${\mathcal{O}}_X$-module over a locally integral prescheme $X$: 6.4.9.
• Elementary symmetric functions of an endomorphism of a finite-type ${\mathcal{O}}_X$-module over a locally Noetherian, reduced prescheme $X$: 6.4.10.
• Elementary symmetric functions of a section of an $\mathcal{A}$-algebra: 6.5.1.
• Essentially integral graded ring: 2.1.11.
• Essentially integral graded ${\mathcal{O}}_Y$-algebra: 3.1.12.
• Essentially reduced graded ring: 2.1.10.
• Essentially reduced graded ${\mathcal{O}}_Y$-algebra: 3.1.12.

F

• Finite morphism: 6.1.1.
• Finite prescheme over a prescheme: 6.1.1.
• Finite quasi-coherent ${\mathcal{O}}_S$-algebra: 6.1.2.
• Finite presentation, graded module of: 2.1.1.
• Finite presentation, graded $\mathcal{S}$-module of: 3.1.1.
• Finite type, graded $\mathcal{S}$-module of: 3.1.1.
• Fractional ideal sheaf: 8.1.2.

G

• Graded algebra over a graded ring: 2.1.2.
• Graded ${\mathcal{O}}_Y$-algebra, essentially integral: 3.1.12.
• Graded ${\mathcal{O}}_Y$-algebra, essentially reduced: 3.1.12.
• Graded prime ideal of $S_{\bullet }$ ($S$ a graded ring): 2.1.10.
• Graded ring, essentially integral: 2.1.11.
• Graded ring, essentially reduced: 2.1.10.
• Graded tensor product of two graded modules: 2.1.2.

H

• Homogenization of a sub-$\mathcal{S}$-module of a graded $\mathcal{S}$-module: 8.13.2.
• Homogeneous prime spectrum of a graded ring: 2.3.1.
• Homogeneous spectrum of a quasi-coherent graded ${\mathcal{O}}_S$-algebra: 3.1.3.
• Homomorphism of graded rings: 2.1.2.
• Homomorphism of degree $k$ of graded modules: 2.1.2.

I

• Ideal of $S_{\bullet }$, graded prime ideal of $S_{\bullet }$ ($S$ a graded ring): 2.1.10.
• Integral closure of a sheaf of rings in an $\mathcal{A}$-algebra: 6.3.2.
• Integral closure of a prescheme $X$ relative to an ${\mathcal{O}}_X$-algebra: 6.3.4.
• Integral morphism: 6.1.1.
• Integral prescheme over a prescheme: 6.1.1.
• Integral quasi-coherent ${\mathcal{O}}_S$-algebra: 6.1.2.
• Integral section (of an $\mathcal{A}$-algebra) over $\mathcal{A}$: 6.3.1.

L

• Locus at infinity of a projective cone: 8.3.3.

M

• Morphism, affine: 1.6.1.
• Morphism, canonical, $G(\mathcal{E})\to \mathrm{Proj}(S)$: 4.5.1.
• Morphism, canonical, $X\to \mathrm{Spec}(\Gamma (X,{\mathcal{O}}_X))$: 5.1.1.
• Morphism, finite: 6.1.1.
• Morphism, integral: 6.1.1.
• Morphism, projective: 5.5.2.
• Morphism, proper: 5.4.1.
• Morphism, quasi-affine: 5.1.1.
• Morphism, quasi-finite: 6.2.3.
• Morphism, quasi-projective: 5.3.1.
• Morphism, Segre: 4.3.1.
• Morphism, universally closed: 5.4.9.

N

• Nilradical of $S_{\bullet }$ ($S$ a graded ring): 2.1.10.
• Nilradical of $\mathcal{S}$ ($\mathcal{S}$ a quasi-coherent graded ${\mathcal{O}}_Y$-algebra): 3.1.12.
• Norm of a section of an $\mathcal{A}$-algebra: 6.5.1.
• Norm of an invertible $\mathcal{A}$-module: 6.5.2.
• Norm of a section of an invertible $\mathcal{A}$-module: 6.5.3.
• Norm of an invertible ${\mathcal{O}}_{X^{\prime }}$-module: 6.5.5.

P

• Periodic graded algebra: 8.14.12.
• Prescheme, affine over a prescheme: 1.2.1.
• Prescheme, blow-up: 8.1.3.
• Prescheme, finite over a prescheme: 6.1.1.
• Prescheme, integral over a prescheme: 6.1.1.
• Prescheme, projective over a prescheme: 5.5.2.
• Prescheme, proper over a prescheme: 5.4.1.
• Prescheme, quasi-affine over a prescheme: 5.1.1.
• Prescheme, quasi-finite over a prescheme: 6.2.3.
• Prescheme, quasi-projective over a prescheme: 5.3.1.
• Projecting cone, affine; projecting cone, projective, of a prescheme $\mathrm{Proj}(\mathcal{S})$: 8.3.1.
• Projective bundle defined by an ${\mathcal{O}}_Y$-module: 4.1.1.
• Projective closure of an affine cone: 8.3.1.
• Projective morphism: 5.5.2.
• Projective prescheme over a prescheme: 5.5.2.
• Proper morphism: 5.4.1.
• Proper part: 5.4.10.
• Proper prescheme over a prescheme: 5.4.1.

Q

• Quasi-affine morphism: 5.1.1.
• Quasi-affine prescheme over a prescheme: 5.1.1.
• Quasi-affine scheme: 5.1.1.

• Quasi-finite morphism: 6.2.3.
• Quasi-finite prescheme over a prescheme: 6.2.3.
• Quasi-projective morphism: 5.3.1.
• Quasi-projective prescheme over a prescheme: 5.3.1.

R

• Radical of an ideal of $S_{\bullet }$ ($S$ a graded ring): 2.1.10.
• Rational geometric fibre of a projective bundle over an extension $K$ of $\kappa (y)$: 4.2.6.
• Retraction, canonical, of a punctured projective cone onto its locus at infinity: 8.3.5.

S

• Section, apex, of an affine (projective) cone: 8.3.3.
• Section, canonical, of ${\mathcal{O}}_X(-1)$ ($X$ a blow-up prescheme): 8.1.9.
• Section, integral (of an $\mathcal{A}$-algebra) over $\mathcal{A}$: 6.3.1.
• Section, zero, of an affine cone: 8.3.3.
• Section, zero, of a vector bundle: 1.7.9.
• Segre morphism: 4.3.1.
• Serre’s criterion: 5.2.1.
• Sheaf, tautological, of a projective bundle: 4.1.1.
• Spectral topology on $\mathrm{Proj}(S)$: 2.3.3.
• Spectrum of an ${\mathcal{O}}_S$-algebra: 1.3.1.
• Spectrum, homogeneous, of a quasi-coherent graded ${\mathcal{O}}_S$-algebra: 3.1.3.
• Spectrum, homogeneous prime, of a graded ring: 2.3.1.
• Symmetric algebra of an $A$-module: 1.7.1.
• Symmetric ${\mathcal{O}}_S$-algebra of an ${\mathcal{O}}_S$-module: 1.7.4.
• Symmetric functions, elementary — see Elementary symmetric functions.

T

• Tautological sheaf of a projective bundle: 4.1.1.
• (TN)-injective, (TN)-surjective, (TN)-bijective (homomorphism of graded modules): 2.7.2.
• (TN)-isomorphism of graded modules: 2.7.2.
• (TN)-injective, (TN)-surjective, (TN)-bijective (homomorphism of graded rings): 2.9.1.
• (TN)-isomorphism of graded rings: 2.9.1.
• (TN)-injective, (TN)-surjective, (TN)-bijective (homomorphism of graded $\mathcal{S}$-modules): 3.4.2.
• (TN)-isomorphism of graded $\mathcal{S}$-modules: 3.4.2.
• (TN)-injective, (TN)-surjective, (TN)-bijective (homomorphism of graded ${\mathcal{O}}_Y$-algebras): 3.6.1.
• (TN)-isomorphism of graded ${\mathcal{O}}_Y$-algebras: 3.6.1.
• Topology, spectral, on $\mathrm{Proj}(S)$: 2.3.3.
• Type, finite, graded $\mathcal{S}$-module of: 3.1.1.

U

• Universally closed morphism: 5.4.9.

V

• Vector bundle defined by an ${\mathcal{O}}_S$-module: 1.7.8.
• Very ample for $q$, very ample for $Y$ (invertible $\mathcal{O}$-module): 4.4.2.

Z

• Zero section of an affine cone: 8.3.3.
• Zero section of a vector bundle: 1.7.9.