Index of notations

Listed in source order of EGA IV. Section numbers refer to the defining occurrence. The four published parts share a single index here; each entry is tagged with its home chapter prefix. Notations from Chapter 0 (continued) live in §§14-23; notations from Chapter IV live in §§1-21. The merged index runs through all four parts (1964, 1965, 1966, 1967).

Chapter 0 (continued)

$dim_{c} (X)$ , $dim (X)$ ( $X$ topological space): 0_IV.14.1.2.
$dim_{x} (X)$ ( $X$ topological space, $x$ point of $X$ ): 0_IV.14.1.2.
$co d im (Y, X)$ ( $X$ topological space, $Y$ closed part of $X$ ): 0_IV.14.2.1.
$co d i m_{x} (Y, X)$ ( $X$ topological space, $Y$ closed part of $X$ , $x$ point of $X$ ): 0_IV.14.2.4.
$N [T_{1}, \dots, T_{n}]$ ( $N$ an $A$ -module): 0_IV.15.1.1.
$dim (A)$ ( $A$ ring): 0_IV.16.1.1.
$h t (a)$ ( $a$ ideal): 0_IV.16.1.3.
$dim_{A} (M)$ , $dim (M)$ ( $M$ an $A$ -module): 0_IV.16.1.7.
$P_{q} (M, n)$ ( $M$ a module of finite type over a Noetherian semi-local ring $A$ , $q$ an ideal of definition of $A$ ): 0_IV.16.2.1.
$p ro f_{m} (M)$ , $p ro f (M)$ ( $M$ an $A$ -module): 0_IV.16.4.5.
$co p ro f_{m} (M)$ , $co p ro f (M)$ ( $M$ an $A$ -module): 0_IV.16.4.9.
$dim . p ro j_{A} (M)$ , $dim . p ro j (M)$ , $dim . in j_{A} (M)$ , $dim . inj (M)$ ( $M$ an $A$ -module): 0_IV.17.2.1.
$dim . co h (A)$ ( $A$ ring): 0_IV.17.2.8.
$dim . p ro j (F)$ , $dim . inj (F)$ ( $F$ a Module on a ringed space): 0_IV.17.2.14.
$dim . co h (X)$ ( $X$ ringed space): 0_IV.17.2.14.
$E \times_{B} F$ ( $B$ , $E$ , $F$ $A$ -rings): 0_IV.18.1.2.
$D_{B} (L)$ ( $B$ ring, $L$ a $B$ -bimodule): 0_IV.18.2.3.
$Y \oplus_{X} Z$ ( $X$ , $Y$ , $Z$ $A$ -bimodules): 0_IV.18.2.7.
$E x a n_{A} (B, L)$ ( $B$ an $A$ -ring, $L$ a $B$ -bimodule): 0_IV.18.3.4.
$E x a n_{A / A^{'}} (B, L)$ : 0_IV.18.3.7.
$E x a l_{A} (B, L)$ , $E x a l_{A / A^{'}} (B, L)$ ( $A$ a commutative ring, $B$ an $A$ -algebra, $L$ a $B$ -bimodule): 0_IV.18.4.1.
$E x a l co m_{A} (B, L)$ , $E x a l co m_{A / A^{'}} (B, L)$ ( $A$ a commutative ring, $B$ a commutative $A$ -algebra, $L$ a $B$ -module): 0_IV.18.4.2.
$H_{A}^{2} (B, L)$ , $H_{A}^{2} (B, L)^{s}$ : 0_IV.18.4.3.
$E x an t o p_{A} (B, L)$ , $E x a lt o p_{A} (B, L)$ , $E x a l co t o p_{A} (B, L)$ : 0_IV.18.5.1.
$E x an t o p_{A / A^{'}} (B, L)$ , $E x a lt o p_{A / A^{'}} (B, L)$ , $E x a l co t o p_{A / A^{'}} (B, L)$ : 0_IV.18.5.2.
$Hom . co n t_{C} (M, N)$ ( $M$ , $N$ topological $C$ -bimodules): 0_IV.18.5.3.
$Der_{A} (B, L)$ ( $B$ an $A$ -ring, $L$ a $B$ -bimodule): 0_IV.20.1.2.
$Der . co n t_{A} (B, L)$ : 0_IV.20.3.1.
$P_{B / A}^{1}$ , $Ω_{B / A}^{1}$ ( $B$ a topological commutative $A$ -algebra): 0_IV.20.4.1.
$P_{B / A}^{n}$ , $Ω_{B / A}^{n}$ ( $B$ a topological commutative $A$ -algebra): 0_IV.20.4.2.
$\hat{P}_{B / A}^{1}$ , $\hat{Ω}_{B / A}^{1}$ ( $B$ a topological commutative $A$ -algebra): 0_IV.20.4.3.
$Ω_{B}$ ( $B$ a topological ring): 0_IV.20.4.3.
$d_{B / A} (x)$ , $d (x)$ , dx, $d_{B / A}$ : 0_IV.20.4.6.
$u_{C / B / A}$ , $v_{C / B / A}$ ( $A$ , $B$ , $C$ rings): 0_IV.20.6.1.
$χ_{E}$ ( $E$ a $B$ -extension $A$ -trivial of $C$ by $L$ ): 0_IV.20.6.8.
$Υ_{B / A /Λ}^{C}$ , $Υ_{B / A}^{C}$ ( $A$ , $B$ , $C$ rings): 0_IV.20.6.14.
$χ_{B /Λ}$ , $χ_{B}$ ( $B$ an $A$ -algebra): 0_IV.20.6.24.
$χ_{E}$ ( $E$ a topological $A$ -algebra): 0_IV.20.7.10.
F_A, $A^{p}$ , $A^{[p]}$ , $E^{[p]}$ ( $A$ a ring of characteristic $p > 0$ , $E$ an $A$ -module): 0_IV.21.1.4.
$Θ_{B / A}$ , $Ξ_{B / A}$ , $π_{B / A}$ , $ω_{B / A}$ ( $A$ , $B$ rings of characteristic $p > 0$ ): 0_IV.21.3.2.
$Δ (L / K, k / k_{0})$ , $d (L / K, k / k_{0})$ , $Δ (L / K, k)$ , $d (L / K, k)$ ( $k_{0}$ , $k$ , $K$ , $L$ fields): 0_IV.21.6.1.
$χ_{B / A}^{'}$ ( $A$ , $B$ rings of characteristic $p > 0$ ): 0_IV.22.4.6.
$A^{(1)}$ ( $A$ an integral Noetherian ring): 0_IV.5.10.17 and IV.7.2.1.

Chapter IV, Part 1

$T^{co n s}$ , $X^{co n s}$ ( $X$ prescheme, $T$ topology of $X$ ): IV.1.9.12.
$f^{co n s}$ ( $f$ morphism of preschemes): IV.1.9.13.

Chapter IV, Part 2

$O (X)$ ( $X$ prescheme): IV.2.2.15 and IV.4.8.1.
$A ss (F)$ ( $F$ an $O_{X}$ -Module): IV.3.1.1.
$d e g . t r_{K} L$ ( $L$ extension of the field $K$ ): IV.4.1.
$λ_{x} (F)$ ( $F$ an $O_{X}$ -Module, $x$ maximal point of $S u pp (F)$ ): IV.4.7.5.
$K (X)$ ( $X$ an $O_{X}$ -Module): IV.4.8.1.
$co d im (Y, X)$ ( $Y$ any part of a prescheme $X$ ): IV.5.1.3.
$dim (F)$ ( $F$ an $O_{X}$ -Module): IV.5.1.12.
$co p ro f (F)$ , $co p ro f (X)$ ( $X$ prescheme, $F$ an $O_{X}$ -Module): IV.5.7.1.
$co p ro f_{m} (M)$ ( $A$ Noetherian ring, $M$ an $A$ -module of finite type): IV.5.7.12.
$p ro f_{X / Z} (F)$ ( $X$ prescheme, $Z$ part of $X$ stable under specialization, $F$ an $O_{X}$ -Module): IV.5.9.1.
$p ro f_{X / Z} (X)$ ( $X$ prescheme, $Z$ part of $X$ stable under specialization): IV.5.9.7.
$p ro f_{T} (F)$ ( $T$ part of a prescheme $X$ , $F$ an $O_{X}$ -Module): IV.5.10.1.
$Z^{(n)} (X)$ ( $X$ prescheme, $n$ integer $⩾ 0$ ): IV.5.10.13.
$A^{(1)}$ ( $A$ an integral Noetherian ring): IV.5.10.17 and IV.7.2.1.
$g r_{J}^{∙} (F)$ ( $F$ an $O_{X}$ -Module, $J$ an Ideal of $O_{X}$ ): IV.6.10.1.
$U_{S_{n}} (F)$ , $U_{C_{n}} (F)$ ( $F$ an $O_{X}$ -Module): IV.6.11.2.
$CM (F)$ ( $F$ an $O_{X}$ -Module): IV.6.11.3.
$U_{S_{n}} (X)$ , $U_{C_{n}} (X)$ , $CM (X)$ ( $X$ prescheme): IV.6.11.4.
$R e g (X)$ , $S in g (X)$ ( $X$ prescheme): IV.6.12.1.
$U_{R_{n}} (X)$ ( $X$ prescheme): IV.6.12.9.
$N or (X)$ ( $X$ prescheme): IV.6.13.1.
$k T_{1}, \dots, T_{n}$ : IV.7.4.8.

Chapter IV, Part 3

$P (X)$ , $Oc (X)$ , $Fc (X)$ , $LFc (X)$ ( $X$ prescheme): IV.8.3.9.
$Q (F)$ ( $F$ an $O_{X}$ -Module): IV.8.5.10.
$Spr (Y)$ , $Spr_{o} (Y)$ , $Spr_{f} (Y)$ ( $Y$ prescheme): IV.8.6.1.
$P ro (C)$ ( $C$ category): IV.8.13.3.
$X_{s}$ , $F^{s}$ , $A^{s}$ , $g^{s}$ , $Z_{s}$ , $h_{s}$ ( $X$ an $S$ -prescheme, $F$ , $A$ $O_{X}$ -Modules, $g$ a homomorphism of $O_{X}$ -Modules, $Z$ part of $X$ , $h : X \to Y$ an $S$ -morphism): IV.9.4.1.
$Q c (X)$ , $L Q c (X)$ , $O (X)$ , $F (X)$ , $O f (X)$ , $LC (X)$ ( $X$ topological space): IV.10.1.1.
$p ro f *_{x} (F)$ , $p ro f *_{Z} (F)$ , $p ro f * (F)$ ( $F$ an $O_{X}$ -Module): IV.10.8.1.
$S (X)$ ( $X$ Jacobson prescheme): IV.10.9.1.
$S (f)$ ( $f$ morphism of Jacobson preschemes): IV.10.9.2.
$Sp m (A)$ , $D_{m} (a)$ ( $A$ Jacobson ring, $a \subset A$ ): IV.10.9.3.
$T or . dim_{B} (M)$ ( $M$ a $B$ -module): IV.12.3.2.

Chapter IV, Part 4

$Y^{(n)}$ , $Y^{(\infty)}$ , $G R_{∙} (f)$ , $N_{Y / X}$ , $O_{Y^{(\infty)}}$ ( $f : Y \to X$ morphism of ringed spaces): IV.16.1.2.
$Y^{(\infty)}$ : IV.16.1.11.
$P_{f}^{n}$ , $P_{X / S}^{n}$ , $P_{f}^{\infty}$ , $P_{X / S}^{\infty}$ , $Ω_{f}^{1}$ , $Ω_{X / S}^{1}$ ( $f : X \to S$ morphism of preschemes): IV.16.3.1.
$d_{f}^{n}$ , $d_{X / S}^{n}$ , $d_{f}^{\infty}$ , $d_{X / S}^{\infty}$ , $d^{n}$ , $d^{\infty}$ , dt, $d_{X / S} (t)$ ( $f : X \to S$ morphism of preschemes): IV.16.3.6.
$P^{n} (u)$ , $G r_{∙} (u)$ , $G r_{n} (u)$ ( $u : X^{'} \to X$ morphism of preschemes): IV.16.4.3.
$Der_{S} (O_{X}, F)$ : IV.16.5.1.
$Der_{S} (O_{X}, F)$ : IV.16.5.4.
$T_{X / S}$ : IV.16.5.7.
$D_{i}$ , $\partial / \partial s_{i}$ : IV.16.5.8.
$T_{X / S}$ : IV.16.5.12.
$T_{X / S} (x)$ , $T_{Y} (s)$ : IV.16.5.13.
$Ω_{X / S}^{p}$ , $Ω_{X / S}^{∙}$ , $Ω_{B / A}^{p}$ ( $p$ integer): IV.16.6.1.
$d$ , $d_{X / S}$ : IV.16.6.3.
$P_{X / S}^{n} (F)$ : IV.16.7.2.
$d_{X / S, F}^{n}$ , $d_{X / S}^{n}$ : IV.16.7.5.
$P_{X / S}^{\infty} (F)$ , $d_{X / S, F}^{\infty}$ : IV.16.7.7.
$D i f f_{X / S}^{n} (F, G)$ , $D i f f_{X / S}^{n}$ , $D i f f_{X / S}^{n} (F, G)$ : IV.16.8.3.
$D i f f_{X / S}^{n}$ , $⟨ t, D ⟩$ : IV.16.8.4.
aD ( $D$ differential operator, $a \in Γ (U, O_{X})$ ): IV.16.8.5.
$D i f f_{X / S} (F, G)$ , $D i f f_{X / S} (F, G)$ : IV.16.8.7.
$D i f f_{X / S}$ : IV.16.8.10.
$∣ p ∣$ , $p!$ , $bin o m (p, q)$ , $z^{p}$ , $ϵ^{p}$ ( $p$ , $q$ multi-indices): IV.16.11.1.
$dim_{x} (f)$ ( $f : X \to Y$ morphism locally of finite type, $x \in X$ ): IV.17.10.1.
$T r_{B / A}$ , $a s t r_{B / A}$ ( $B$ finite and free $A$ -algebra): IV.18.2.1.
$T r_{B / O_{X}}$ , $a s t r_{B / O_{X}}$ , $T r_{B / O_{X}, U}$ , $a s t r_{B / O_{X}, U}$ ( $X$ ringed space, $B$ an $O_{X}$ -Algebra locally free of finite rank): IV.18.2.2.
$T r_{f}$ ( $f$ finite and étale morphism): IV.18.2.6.
$d_{X / Y}$ , $D_{X / Y}$ : IV.18.2.7.
$V$ : IV.18.5.1.
$A l (X, \overset{ˇ}{E}, I)$ , $Al (E, I)$ : IV.18.5.2.
$O f (S^{'})$ , $Of (X)$ , $I d (B^{'})$ : IV.18.5.3.
$Hom . l oc (A, B)$ : IV.18.6.1.
$^{h} A$ : IV.18.6.5 and IV.18.6.7.
$Hom . s l oc (A, B)$ : IV.18.6.7.
$^{h s} A_{(i)}$ , $^{h s} A$ : IV.18.8.7 and IV.18.8.9.
$co d i m_{y}^{t} (Y, X)$ : IV.19.1.3.
$p ro f_{T, t} (F)$ , $p ro f_{T} (F)$ : IV.19.9.1.
$O_{X} [S^{- 1}]$ , $F [S^{- 1}]$ : IV.20.1.1.
$S (O_{X})$ , $M_{X}$ , $M (X)$ , $M_{X} (F)$ , $M (X, F)$ : IV.20.1.3.
$d o m (ϕ)$ ( $ϕ$ meromorphic function): IV.20.1.4.
$d o m (u)$ ( $u$ meromorphic section of $F$ ): IV.20.1.7.
$(M_{X} (L))^{\times}$ ( $L$ an invertible $O_{X}$ -Module): IV.20.1.8.
$s^{- 1}$ ( $s$ meromorphic section of an invertible $O_{X}$ -Module): IV.20.1.10.
$M_{f} (O_{X})$ , $M_{f}$ ( $f$ morphism of ringed spaces), $ϕ \circ f$ ( $ϕ$ meromorphic function), $u \circ f$ ( $u$ meromorphic section of $F$ ), $M_{f} (F)$ : IV.20.1.11.
Ps.hom(X, Y), $P s . h o m_{S} (X, Y)$ : IV.20.2.1.
$ω ∣ U$ ( $ω$ pseudo-morphism), $P s . h o m (X, Y)$ , $P s . h o m_{S} (X, Y)$ : IV.20.2.2.
$d o m_{S} (ω)$ , $d o m (ω)$ ( $ω$ pseudo-morphism): IV.20.2.3.
$M_{X}^{'}$ , M'(X): IV.20.2.8.
$f \circ ω$ ( $f$ morphism, $ω$ pseudo-morphism): IV.20.3.1.
$ω \circ f$ ( $f$ morphism, $ω$ pseudo-morphism): IV.20.3.2.
$P s . h o m_{S} (X, Y)_{f}$ , $P s . h o m_{S} (X, Y)_{f}$ : IV.20.3.2.
$Γ_{ω}$ ( $ω$ pseudo-morphism): IV.20.4.1.
$p^{- 1}$ ( $p : Γ \to X$ restriction of the first projection): IV.20.4.2.
$ω (M)$ ( $ω$ pseudo-morphism, $M$ part of $X$ ): IV.20.4.2.
$P s . h o m_{X / S} (X, Y)$ : IV.20.5.1.
$P s . h o m_{X / S} (X, Y)$ : IV.20.5.3.
$M_{X / S}^{'}$ , $M^{'} (X / S)$ : IV.20.5.4.
$S_{X / S} (U)$ , $S_{X / S}$ , $M_{X / S}$ , $M (X / S)$ : IV.20.6.1.
$M_{X / S} (F)$ , $M (X / S, F)$ : IV.20.6.2.
$M_{X / S}^{\times} (U)$ , $M_{X / S}^{\times}$ , $D i v_{X / S, f}$ : IV.20.6.7.
$D i v_{X}$ , $Div (X)$ , $d i v (f)$ , $d i v_{X} (f)$ ( $X$ ringed space): IV.21.1.2.
$S u pp (D)$ ( $D$ divisor): IV.21.1.2.
$Div (A)$ ( $A$ ring): IV.21.2.1.
$d i v (s)$ ( $s$ section of an invertible Module): IV.21.1.4.
$D i v_{X}^{+}$ , $Div^{+} (X)$ , $D ⩽ D^{'}$ ( $D$ , $D^{'}$ divisors): IV.21.1.6.
Id.inv(X), $Id . inv_{X}$ : IV.21.2.4.
$J (f)$ , $J (f) = O_{X} \cdot f$ : IV.21.2.5.
$d i v (J)$ ( $J$ fractional Ideal): IV.21.2.6.
$O_{X} (D)$ ( $D$ divisor): IV.21.2.8.
$s_{D}$ ( $D$ divisor): IV.21.2.9.
$D (X)$ , $c l (L, s)$ : IV.21.2.10.
$Y (D)$ ( $D$ positive divisor): IV.21.2.12.
$Div . p r in c (X)$ : IV.21.3.1.
$Pic (X)$ , $c l (L)$ , $l$ , $l^{'}$ , $Pic (f)$ : IV.21.3.2.
$f^{*} (D)$ ( $f$ morphism of ringed spaces, $D$ divisor), $Div_{f} (X)$ : IV.21.4.2.
$M_{X}^{f \times}$ , $D i v_{X}^{f}$ : IV.21.4.3.
$N_{X^{'} / X} (s^{'})$ , $N_{X^{'} / X} (L^{'})$ ( $s^{'}$ meromorphic section of an invertible $O_{X^{'}}$ -Module): IV.21.5.3.
$f_{*} (D^{'})$ , $N_{X^{'} / X} (D^{'})$ ( $f$ finite morphism, $D^{'}$ divisor on $X^{'}$ ): IV.21.5.5.
$J (X)$ , $z (X)$ , $z^{+} (X)$ ( $X$ locally Noetherian prescheme): IV.21.6.1.
$m u l t_{x} (Z)$ , $S u pp (Z)$ , $dim (Z)$ , $co d im (Z)$ ( $Z$ cycle): IV.21.6.1.
$X^{(p)}$ , $z^{p} (X)$ , $z^{p +} (X)$ : IV.21.6.2.
$Z ∣ U$ ( $Z$ cycle), $z_{X}$ , $z_{X}^{p}$ , $z_{X}^{+}$ , $z_{X}^{p +}$ : IV.21.6.3.
$c$ : IV.21.6.4.
$cyc (D)$ ( $D$ divisor): IV.21.6.5 and IV.21.6.7.
$m u l t_{x} (D)$ , $m u l t_{\overline{x}} (D)$ ( $D$ divisor), $ω_{x} (f)$ ( $f$ regular meromorphic function): IV.21.6.7.
$Z^{+} (f)$ , $Z^{-} (f)$ , $z_{p r in c}^{1} (X)$ , $Cl (X)$ : IV.21.6.7.
$Y (C)$ , Y'(C), $J_{X} (C)$ , $J (C)$ ( $C$ positive 1-codimensional cycle): IV.21.7.1.
$f^{*} (Z)$ ( $Z$ 1-codimensional cycle, $f$ morphism): IV.21.10.3 and IV.21.10.11.
$Γ_{T} (J_{X}^{1})$ : IV.21.10.3.
$f_{*} (Z^{'})$ ( $Z^{'}$ 1-codimensional cycle, $f$ finite morphism): IV.21.10.14.
$Λ^{m a x} E$ ( $E$ locally free Module): IV.21.11.1.
$U^{\circ}$ , $A ff (U / X)$ : IV.21.12.1.
$D a f (U / X)$ : IV.21.12.5.
$D i v_{X / S}$ , $Div (X / S)$ : IV.21.15.2.
$D i v_{X / S}^{+}$ , $Div^{+} (X / S)$ : IV.21.15.3.
$S_{X / S}$ : IV.21.15.3.
$Div_{X / S} (S^{'})$ , $Div_{X / S}^{+} (S^{'})$ ( $S^{'}$ an $S$ -prescheme): IV.21.15.9.