Index of notation

A reference index of notation used throughout SGA 1. Locators are given as <Exposé Roman>.<section>(.<sub>) or $< E x p os \overset{e}{ˊ} R o man > (p . < p a g e >)$ when known; the source's OCR-extracted index does not carry page locators, so the locator column reconstructs them from first use in the relevant Exposé. Where the OCR mangled an identifier (most commonly by dropping the $π$ prefix in $π_{1} (...)$ or the script-O / hat over a category), the original symbol is restored and the restoration noted. Unresolved cases are marked with a translator note rather than silently fixed.

Sheaves of differentials and infinitesimal neighborhoods (Exposés II–III)

Notation	Where introduced
$Δ_{X / Y}$ , or simply $Δ$	II.1
$Ω_{X / Y}^{1}$ (sheaf of relative differentials)	II.1
$P_{X / Y}^{n}$ (sheaf of principal parts of order $n$ )	II.1
$Δ_{X / Y}^{n}$ (n-th infinitesimal neighborhood of the diagonal)	II.1
$m Δ_{X / Y}$ (ideal sheaf of the diagonal)	II.1
$d_{X / S}^{n}$ (n-th differential / iterated differential)	II
$m g_{X / S}$	II

Categories, morphisms, and 2-categorical infrastructure (Exposé VI)

Notation	Where introduced
`C(...)` (a category)	VI
`Pro-C(...)` (pro-objects of $C$ )	VI
$Γ$ (sections / global-section functor; context-dependent)	VI
`(Ens)` (category of sets)	VI
`Cat` (category of categories)	VI
$O b (C)$ (objects of $C$ )	VI
$Fl (C)$ (arrows / "fleches" of $C$ )	VI
$Hom (C, C^{'})$ (functors $C \to C^{'}$ )	VI
$C^{\circ}$ (opposite category)	VI
$C a t_{/ E}$ (categories over $E$ / fibered over $E$ )	VI
$Hom_{E / -} (F, G)$ (cartesian functors over $E$ )	VI
$v * u$ (vertical composition of 2-cells / Godement product)	VI
$F \times_{E} G$ (fibre product of fibered categories)	VI
$f^{*} : C a t_{/ E} \to C a t_{/ E^{'}}$ (base change of fibered categories)	VI
$Γ (G / E)$ , `Γ̲(G/E)` (sections / sheaf of sections of a fibered category)	VI
`F_S` (fibre of a fibered category over $S$ )	VI
$f_{F}^{} (...)$ or $f^{} (...)$ (inverse image along $f$ )	VI
$Γ_{f} (...)$	VI
$Hom_{∙} (F, G)$	VI
$\hat{C} a t_{/ E}$ (a hatted variant — pseudo-functorial 2-category)	VI
$F / E$ (fibered category $F$ over $E$ )	VI
$f_{}^{F}$ or $f_{}$ (direct image; "tilde" variant)	VI

Notation	Where introduced
$π_{1} (S, a)$ (fundamental group at the geometric point $a$ )	V
$π_{1} (S; a, a^{'})$ (set of paths from $a$ to $a^{'}$ )	V
$π_{1} (f; a^{'})$ (induced morphism on fundamental groups)	V
$C (S)$ (category of finite étale covers of $S$ )	V
`Sch` (category of schemes)	V
$μ_{n, S}$ (group scheme of $n$ -th roots of unity over $S$ )	XI
$X^{an}$ , $f^{an}$ (analytification)	XII
`SF` or $S (F)$ (sheaf associated to a presheaf $F$ )	XII
$H_{t}^{1} (U, F)$ (Čech $H^{1}$ for the topology $t$ )	XII
$R_{t}^{1} g_{*} F$ (higher direct image for the topology $t$ )	XII
$C_{t} ((U, X) / S)$ or $C_{t}$ (category for the topology $t$ )	XII
$π_{1}^{t} ((U, X) / S, a)$ , $π_{1}^{t} (U, a)$ , $π_{1}^{t} (U)$ (fundamental group for $t$ )	XIII
$(g_{*}^{t} Φ)_{T^{'}}$	XIII
$H^{0} (V, C_{V})^{Π}$	XIII
$π_{1}^{L} (U, a)$ (fundamental group with prime-to- $L$ coefficients)	XIII
$π_{1}^{'} (X, a)$ (a derived / first variant of $π_{1}$ )	XIII
$π_{1}^{L} (X / S, g, \overset{s}{ˉ})$ or $π_{1}^{L} (X / S, g)$ (fundamental group of a relative scheme)	XIII
$π_{1}^{L} (X_{\overset{s}{ˉ}}, a)_{K}$ (fundamental group of a geometric fibre, base extension to $K$ )	XIII
$Z_{ℓ} [1]$ (a Tate-twist–like degree shift)	XIII

Séminaire de Géométrie Algébrique du Bois-Marie — English

Index of notation

Sheaves of differentials and infinitesimal neighborhoods (Exposés II–III)

Categories, morphisms, and 2-categorical infrastructure (Exposé VI)

Fundamental group (Exposé V) and étale-topology refinements (Exposé XIII)