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P Ò
M[ϕ] (Ù¥ M ´ B �, ϕ : A → B ´�Ó�) : 0, 1.0.2.
BI, IB (Ù¥ I ´� A �n�, ����l A � B �Ó�) : 0, 1.0.3.
r(a) (Ù¥ a ´n�) : 0, 1.1.1.
R(A) (Ù¥ A ´�) : 0, 1.1.2.
Sf (Ù¥ f ´��� A ���) : 0, 1.2.1.
S−1A, S−1M, m/s, iSA, iSM , iS (Ù¥ A ´�, M ´ A �, S ´ A �¦5f8) : 0, 1.2.2.
Af , Mf , Ap , Mp (Ù¥ M ´ A �, f ∈ A , p ´ A ��n�) : 0, 1.2.3.
S−1t (Ù¥ u ´ A �Ó�, S ´ A �¦5f8) : 0, 1.3.1.
ρT,SA , ρT,S
M , ρT,S (Ù¥ M ´ A �, S Ú T ´ A �¦5f8) : 0, 1.4.1.
Supp(M) (Ù¥ M ´ A �) : 0, 1.7.1.
F |U , u|U (Ù¥ F ´ X þ��, u ´ X þ����, U ´ X �m8) : 0, 3.1.5.
Fx, sx, Γ(U, F ), u(s), Supp F (Ù¥ F ´ X þ�8Ü�, x ´ X �:, U ´ X �m8, s ´Γ(U, F ) ���, u ´ X þ��Ó�) : 0, 3.1.6.
ψ∗F (Ù¥ F ´ X þ��, ψ : X → Y ´ëYN�) : 0, 3.4.1.
ψ∗(u) (Ù¥ u ´ X þ����) : 0, 3.4.2.
ψx : 0, 3.4.4.
G → F (Ù¥ F ´ X þ��, G ´ Y þ��) : 0, 3.5.1.
u], v[, ρG : 0, 3.5.3.
ψ∗G , ψ∗(v), σF : 0, 3.5.5.
OX , OX,x, Ox, 1, e (Ù¥ X ´�È�m) : 0, 4.1.1.
F ,Vp F (Ù¥ F ´ OX ��) : 0, 4.1.5.
J F (Ù¥ J ´ OX �n��, F ´ OX ��) : 0, 4.1.6.
Ψ∗F , Ψ∗(u) (Ù¥ F ´ OX ��, u ´ OX ��Ó�) : 0, 4.2.1.
220 P Ò
Ψ∗C (Ù¥ C ´ OX �ê�) : 0, 4.2.4.
Ψ∗G , Ψ∗(v) (Ù¥ G ´ OY ��, v ´ OY ��Ó�) : 0, 4.3.1.
Ψ∗C (Ù¥ C ´ OY �ê�) : 0, 4.3.4.
(Ψ∗J )A , J A (Ù¥ J ´ B �n��) : 0, 4.3.5.
G → F (Ù¥ F ´ OX ��, G ´ OY ��) : 0, 4.4.1.
u]θ, u
], v[θ, v
[, ρG , σF : 0, 4.4.3.
u1 ⊗ u2 (Ù¥ u1, u2 ´ OY ��� OX ���Ó�) : 0, 4.4.4.
L −1 (Ù¥ L ´�_ OX ��) : 0, 5.4.3.
L ⊗n (Ù¥ L ´�_ OX ��) : 0, 5.4.4.
Γ∗(L ), Γ∗(L , F ) (Ù¥ L ´�_ OX ��, F ´ OX ��) : 0, 5.4.6.
O∗X : 0, 5.4.7.
mx, k(x), f(x) : 0, 5.5.1.
Xf : 0, 5.5.2.
Im(M ′ ⊗A N ′) (Ù¥ M ′, N ′ ©O´ M, N � A f�) : 0, 6.0.
bA, cM : 0, 7.2.3 Ú 7.3.1.
A{T1, . . . , Tr} : 0, 7.5.1.
A{S−1} : 0, 7.6.1.
a{S−11} (Ù¥ a ´ A �mn�) : 0, 7.6.9.
A{f}, a{f} : 0, 7.6.15.
A{S} : 0, 7.6.15.
(M ⊗A N)b, M b⊗AN : 0, 7.7.1.
ub⊗v : 0, 7.7.3.
Spec A, jx, mx, k(x), f(x), Mx, r(E), V (E), V (f), D(f) (Ù¥ A ´�, M ´ A �, f ∈ A ,
E ⊆ A , x ∈ Spec A ) : I, 1.1.1.
j(Y ) (Ù¥ Y ⊆ Spec A ) : I, 1.1.3.aϕ (Ù¥ ϕ ´�Ó�) : I, 1.2.1.
S′f (Ù¥ f ´����) : I, 1.3.1.
ρg,f (Ù¥ f, g ´����) : I, 1.3.3.
eA, fM, θf (Ù¥ A ´�, f ∈ A , M ´ A �) : I, 1.3.4.
eu (Ù¥ u ´ A �Ó�) : I, 1.3.5.
eϕ ( ϕ ´�Ó�) : I, 1.6.1.
A(X) (Ù¥ X ´��V/) : I, 1.7.1.
OX/Y (Ù¥ X ´V/) : I, 2.1.6.
Hom(X, Y ) (Ù¥ X, Y ´V/) : I, 2.2.1.
HomS(X, Y ), 1X (Ù¥ X, Y ´ S V/) : I, 2.5.2.
Γ(X/S) (Ù¥ S ´V/, X ´ S V/) : I, 2.5.5.
X t Y (Ù¥ X, Y ´V/) : I, 3.1.
X ×S Y, X × Y, (g, h)S , u ×S v, u × v (Ù¥ X, Y ´ S V/, g, h, u, v ´ S ��) : I, 3.2.1.
X ×A Y, X ⊗A B, (g, h)A, u ×A v (Ù¥ X, Y ´ A V/, A ´�, B ´ A �ê, g, h, u, v ´
P Ò 221
A ��) : I, 3.2.1.
X(S′) (Ù¥ X, S′ ´ S V/) : I, 3.3.6.
f(S′) (Ù¥ S′ ´ S V/, f ´ S ��) : I, 3.3.7.
Γf (Ù¥ f ´ S ��) : I, 3.3.14.
X(T ) (Ù¥ X, T ´V/) : I, 3.4.1.
P ×R Q (Ù¥ P, Q ´ R þ�8Ü) : I, 3.4.2.
X(T )S (Ù¥ X, T ´ S V/) : I, 3.4.3.
X(B), X(B)A (Ù¥ X ´ A V/, B ´ A �ê) : I, 3.4.4.
X ⊗Y B, X ⊗OY B (Ù¥ B ´ Oy �ê, Ù¥ y ∈ Y ) : I, 3.6.2.
Z 6 Y (Ù¥ Y, Z ´,V/�ü�fV/) : I, 4.1.10.
f−1l(Y ′) (Ù¥ f : X → Y ´��, Y ′ ´ Y �fV/) : I, 4.4.1.
NX (Ù¥ X ´V/) : I, 5.1.1.
Xred (Ù¥ X ´V/) : I, 5.1.3.
fred (Ù¥ f ´��) : I, 5.1.5.
∆X|S , ∆X , ∆ (Ù¥ X ´ S V/) : I, 5.3.1.
rgK(X) (Ù¥ K ´�, X ´k� K V/) : I, 6.4.5.
n(X) (Ù¥ X ´�þ�k�V/) : I, 6.4.8.
Γrat(X/Y ) : I, 7.1.2.
R(X) (Ù¥ X ´V/) : I, 7.1.3.
R(X) (Ù¥ X ´V/) : I, 7.3.2.
L(A) (Ù¥ A ´��) : I, 8.1.2.
δ(f) (Ù¥ f ´knN�) : I, 8.2.1.
F ⊗OS G , F ⊗S G (Ù¥ F , G ´ü� S V/þ���) : I, 9.1.2.
G (Ù¥ G ´ OX ��) : I, 9.4.1.
Y (Ù¥ Y ´fV/) : I, 9.5.10.
Spf A, OX (Ù¥ A ´�N�, X = Spf A ) : I, 10.1.2.
D(f) (Ù¥ f ´�N����) : I, 10.1.4.aϕ, eϕ (Ù¥ ϕ ´�N��ëYÓ�) : I, 10.2.1.
I∆ (Ù¥ I ´½Ân�) : I, 10.3.1.
X ×S Y (Ù¥ X, Y ´ S /ªV/) : I, 10.7.3.
F/X′ , cF , u/X′ , bu (Ù¥ F ´ OX ��, u ´ OX ��Ó�, X ′ ´ X �4f8) : I, 10.8.4.
X/X′ , bX (Ù¥ X ´V/, X ′ ´ X �4f8) : I, 10.8.5.
bf (Ù¥ f ´V/��) : I, 10.9.1.
M∆, u∆ (Ù¥ M ´?�� A þ��, u ´ A ��ëYÓ�) : I, 10.10.1.
∆X|S , ∆X (Ù¥ X ´ S /ªV/) : I, 10.15.1.
¢ Ú
A �ê [ A-algebre / A-algebra ],
(0, 1.0.4), 2
— k� A �ê, 3 A þk���ê [ A-algebre finie, algebre finie sur A / finite A-algebra,
algebra finite over A ],
(0, 1.0.5), 2
— k��. A �ê, 3 A þk��.��ê [ A-algebre entiere finie, algebre entiere finie
sur A / algebra finite (integral) over A ],
(0, 1.0.5), 2
— �. A �ê, 3 A þ�.��ê [ A-algebre entiere, algebre entiere sur A / algebra
integral over A ],
(0, 1.0.5), 2
A V/, A þ�V/ (Ù¥ A ´�) [ A-schema, schema au-dessus de A / A-scheme, scheme
over A ],
(I, 2.5.1), 100
A V/���3 A �ê¥�:, B � A : (Ù¥ B ´ A �ê) [ point d’un A-schema a valeurs
dans un A-algebre / point of an A-scheme with values in an A-algebra ],
(I, 3.4.4), 110
A V/���, A �� [morphisme de A-schemas, A-morphisme / morphism of A-schemes,
A-morphism ],
(I, 2.5.2), 100
A �3 Spec A þ��)� [ faisceau associe a un A-module sur Spec A / sheaf over Spec A
associated to an A-module ],
(I, 1.3.4), 77
¢ Ú 223
A þ�/ªV/, A /ªV/ (Ù¥ A ´�N�) [ schema formel au-dessus de A, A-schema
formel / formal scheme over A, formal A-scheme ],
(I, 10.4.7), 188
A �ê� (Ù¥ A ´����) [ A -Algebre / A -algebra ],
(0, 4.1.3), 27
A n�� (Ù¥ A ´��) [ A -Ideaux / A -ideal ],
(0, 4.1.3), 27
A �� (Ù¥ A ´��) [ A -Module / A -module ],
(0, 4.1.3), 27
— A ���éó [ dual d’un A -Module / dual of an A -module ],
(0, 4.1.5), 28
— A ��� p g� (Ù¥ A ´����) [ puissance exterieur p-eme d’un A -Module /
p-th exterior power of an A -module ],
(0, 4.1.5), 28
— ©g A �� (Ù¥ A ´©g��) [ A -Module gradue / graded A -module ],
(0, 4.1.4), 28
A f��¤)¤� A f�ê� [ sous-A -Algebre engendree par un sou-A -Module / sub-A -
algebra generated by a sub-A -module ],
(0, 4.1.3), 27
B ��� A ��� Ψ �� [ Ψ-morphisme d’un B-Module dans un A -Module / Ψ-morphism
of an B-Module to an A -module ],
(0, 4.4.1), 32
I ?�ÿÀ ( I ?ÿÀ) 1©, I ý?�ÿÀ ( I ý?ÿÀ) [ topologie I-adique, topologie I-preadique
/ I-adic topology, I-preadic topology ],
(0, 7.1.9), 53
K V/� K kn: [ point rationnel sur K d’un K-schema / rational point over K of a K-
scheme ],
(I, 3.4.5), 111
Noether 8B{ [ principe de recurrence noetherienne / noetherian induction principle ],
(0, 2.2.2), 13
OX �ê� (Ù¥ (X, OX) ´�È�m) [ OX-Algebre / OX -algebra ],
(0, 5.1.3), 35
— [và OX �ê� [ OX-Algebre quasi-coherent / quasi-coherent OX -algebra ],
(0, 5.1.3), 35
— và OX �ê� [ OX-Algebre coherent / coherent OX -algebra ],
(0, 5.3.7), 38
— OX �ê��Å"� [Nilradical d’une OX-Algebre / nilradical of an OX -algebra ],
1©5¿, ·�3¦^“?�ÿÀ”ù�c��ÿ, ob�T�½�´©l����. ù�Ï~�^{Ø���.
224 ¢ Ú
(I, 5.1.1), 126
OX �ü ��¡ [ section unite de OX / unity section of OX ],
(0, 4.1.1), 26
OX �� (Ù¥ (X, OX) ´�È�m) [ OX-Module / OX -module ],
(0, 5.1.1), 35
— f ²"� OX �� [ OX-Module f-plat / f -flat OX -module ],
(I, 6.7.1), 50
— OX ���"zf [ annulateur d’un OX-Module / annihilator of an OX -module ],
(0, 5.3.7), 38
— ÛÜgd OX �� [ OX-Module localement libre / locally free OX -module ],
(0, 5.4.1), 39
— �_ OX �� [ OX-Module inversible / invertible OX -module ],
(0, 5.4.1), 39
— �_ OX ���_ [ inverse d’un OX-Module inversible / inverse of an invertible OX -
module ],
(0, 5.4.3), 40
— [và OX �� [ OX-Module quasi-coherent / quasi-coherent OX -module ],
(0, 5.1.3), 35
— và OX �� [ OX-Module coherent / coherent OX -module ],
(0, 5.3.1), 37
— d�x�N�¡¤)¤� OX �� [ OX-Module engendre par une famille de sections
globales / OX -module generated by a family of global sections ],
(0, 5.1.1), 35
— k�¥« OX �� [ OX-Module admet une presentation finie / OX -module of finite
presentation ],
(0, 5.2.5), 37
— k�. OX �� [ OX-Module de type fini / OX -module of finite type ],
(0, 5.2.1), 36
OXi ���ÝK4� [ limite projective de OXi -Modules / projective limit of OXi -module ],
(I, 10.6.6), 193
S V/, S þ�V/ (Ù¥ S ´V/) [ S-schema, schema au-dessus de S / S-scheme, scheme
over S ],
(I, 2.5.1), 100
— S V/�(��� [morphisme structural d’un S-schema / structure morphism of an
S-scheme ],
(I, 2.5.1), 100
— S V/���, S �� [morphisme de S-schemas, S-morphisme / morphism of S-
schemes, S-morphism ],
(I, 2.5.2), 100
¢ Ú 225
— ©l S V/, 3 S þ©l�V/ [ schema separe au-dessus de S / scheme separated over
S ],
(I, 5.4.1), 134
— k�. S V/, 3 S þk�.�V/ [ S-schema de type fini, schema de type fini sur S /
S-scheme of finite type, scheme of finite type over S ],
(I, 6.3.1), 144
S V/���3 S V/¥�:, T � S : (Ù¥ T ´ S V/) [ point d’un S-schema a valeurs
dans un S-schema / point of an S-scheme with values in an S-scheme ],
(I, 3.4.3), 109
S V/� S �¡ [ S-section d’un S-schema / S-section of an S-scheme ],
(I, 2.5.5 Ú 5.3.11), 101, 132
S V/� S kn�¡ [ S-section rationnelle d’un S-schema / rational S-section of an S-
scheme ],
(I, 7.1.2), 155
S V/� u: s ∈ S �þ�: [ point d’un S-schema au-dessus d’un point s ∈ S / point of
an S-scheme above a point s ∈ S ],
(I, 2.5.1), 100
S V/� u s ∈ S �þ� K �: [ point d’un S-schema a valeurs dans K au-dessus de s ∈ S
/ point of an S-scheme with values in K above s ∈ S ],
(I, 3.4.5), 110
S �¡�� [ image d’une S-section / image of an S-section ],
(I, 5.3.11), 132
S þ�/ªV/, S /ªV/ (Ù¥ S ´/ªV/) [ schema formel au-dessus de S, S-schema
formel / formal scheme over S, formal S-scheme ],
(I, 10.4.7), 188
— S /ªV/�(��� [morphisme structural d’un S-schema formel / structure mor-
phism of formal S-scheme ],
(I, 10.4.7), 188
— ©l S /ªV/, 3 S þ©l�/ªV/ [ schema formel separe au-dessus de S / formal
scheme that is separated over S ],
(I, 10.15.1), 215
— k�. S /ªV/, 3 S þk�.�/ªV/ [ S-schema formel de type fini, schema
formel de type fini sur S / formal S-scheme of finite type, formal scheme of finite
type over S ],
(I, 10.13.3), 211
S /ªV/�n�È [ produit fibre de S-schemas formels / fibred product of formal S-
schemes ],
(I, 10.7.1), 195
X ×S X �é�� [ diagonale de X ×S X / diagonal of X ×S X ],
226 ¢ Ú
(I, 5.3.9), 132
Zariski ÿÀ (ÌÿÀ) [ topologie de Zariski / Zariski topology ],
(I, 1.1.2), 73
B
4: [ point ferme / closed point ],
(0, 2.1.3), 12
4/ªfV/ [ sous-schema formel ferme / closed formal subscheme ],
(I, 10.14.2), 213
Ø��©| [ composante irreductible / irreducible component ],
(0, 2.1.6), 12
ØÓV/þ���ÜþÈ [ produit tensoriel de faisceaux sur des schemas distincts / tensor
product of sheaves over distinct schemes ],
(I, 9.1.2), 170
C
� [ faisceau / sheaf ],
(, )
— K ��, ��3�Æ K ¥�� [ faisceau a valeurs dans une categorie K / sheaf with
values in a category K ],
(0, 3.1.2), 14
— OX ���L� (Ù¥ X ´�V/) [ faisceau de torsion d’un OX-Module / torsion sheaf
of an OX -module ],
(I, 7.4.1), 164
— L�, L OX �� (Ù¥ X ´�V/) [ faisceau de torsion / torsion sheaf ],
(I, 7.4.1), 164
— ~�� [ faisceau constant / constant sheaf ],
(0, 3.6.1), 24
— ©g�� [ faisceau d’anneaux gradues / sheaf of graded rings ],
(0, 4.1.4), 28
— Q���, 3�:?Q���� [ faisceau d’anneaux reduit, faisceau d’anneaux reduit en
un point / sheaf of reduced rings, sheaf of rings reduced at a point ],
(0, 4.1.4), 28
— c\� [ faisceau induit / induced sheaf ],
(0, 3.7.1), 25
— ÛÜ~�� [ faisceau localement constant / locally constant sheaf ],
(0, 3.6.1), 24
— ÅÜ ¤�� [ faisceau obtenu par recollement / sheaf obtained by glueing ],
¢ Ú 227
(0, 3.3.1), 19
— và�� [ faisceau coherent d’anneaux / coherent sheaf of rings ],
(0, 5.3.7), 38
— ÿÀÄþ�� [ faisceau definis sur une base d’ouverts / sheaf defined on a base of open
sets ],
(0, 3.2.2), 17
— �lÑ� [ faisceau pseudo-discret / pseudo-discrete sheaf ],
(0, 3.8.1), 26
— ÃL OX �� (Ù¥ X ´�V/) [ OX-Module sans torsion / torsion-free OX -module ],
(I, 7.4.1), 164
— ý��©Y� [ faisceau associe a un prefaisceau / sheaf associated to a presheaf ],
(0, 3.5.6), 23
— 3m8þ�c\� [ faisceau induit sur un ouvert / sheaf induced on an open set ],
(0, 3.1.5), 15
— �5��, 3�:?�5��� [ faisceau d’anneaux normal, faisceau d’anneaux normal
en un point / sheaf of normal rings, sheaf of rings normal at a point ],
(0, 4.1.4), 28
— �K��, 3�:?�K��� [ faisceau d’anneaux regulier, faisceau d’anneaux regulier
en un point / sheaf of regular rings, sheaf of rings regular at a point ],
(0, 4.1.4), 28
���¡ [ section d’un faisceau / section of a sheaf ],
(0, 3.1.6), 16
��ª^ [fibre d’un faisceau / stalk of a sheaf ],
(0, 3.1.6), 16
D
�ê K V/ (Ù¥ K ´�) [ K-schema algebrique / algebraic K-scheme ],
(I, 6.4.1), 147
— �êV/�Ä� [ corps de base d’un schema algebrique / base field of an algebraic
scheme ],
(I, 6.4.1), 147
— ©l�ê K V/ [ K-schema algebrique separe / separated algebraic K-scheme ],
(I, 6.4.1), 147
— k� K V/, 3 K þk��V/ [ K-schema fini, schema fini sur K / finite K-scheme,
scheme finite over K ],
(I, 6.4.5), 148
�ê���ÜþÈ [ produit tensoriel complete d’algebres / complete tensor product of alge-
bras ],
(0, 7.7.5), 68
228 ¢ Ú
:�AÏz [ specialisation d’un point / specialization of a point ],
(0, 2.1.2), 12
:���z [ generisation d’un point / generization of a point ],
(0, 2.1.2), 12
;�¹\ [ injection canonique / canonical injection ],
(, )
— /ªfV/�;�¹\ [ injection canonique d’un sous-schema formel / canonical injec-
tion of a formal subscheme ],
(I, 10.14.2), 213
— fV/�;�¹\ [ injection canonique d’un sous-schema / canonical injection of a
subscheme ],
(I, 4.1.7), 119
— f�mþ�p��È�m�;�¹\ [ injection canonique d’un espace annele induit sur
un partie / canonical injection of an induced ringed space on a subspace ],
(0, 4.1.2), 27
F
��V/ [ schema affine / affine scheme ],
(I, 1.7.1), 89
— ��V/�� [ anneau d’un schema affine / ring of an affine scheme ],
(I, 1.7.1), 89
— ��V/�(�� [ faisceau structural d’un schema affine / structure sheaf of an affine
scheme ],
(I, 1.3.4), 77
��m8 [ ouvert affine / affine open set ],
(I, 2.1.1), 94
��/ªm8, ?���/ªm8, Noether ��/ªm8 [ ouvert formel affine, ouvert formel
affine adique, ouvert formel affine noetherien / affine formal open set, adic affine
formal open set, noetherian affine formal open set ],
(I, 10.4.1), 187
G
V/ [ schema / scheme ],
(I, 2.1.2), 94
— Artin V/ [ schema artinien / artinian scheme ],
(I, 6.2.1), 143
— Noether V/ [ schema noetherien / noetherian scheme ],
(I, 6.1.1), 140
¢ Ú 229
— Ø��V/ [ schema irreductible / irreducible scheme ],
(I, 2.1.8), 95
— ©lV/ [ schema separe / separated scheme ],
(I, 5.4.1), 134
— V/�Q�zV/ [ schema reduit associe a un schema / reduced scheme associated to
a scheme ],
(I, 5.1.3), 126
— V/3�:?�ÛÜV/ [ schema local en un point d’un schema / local scheme at a
point of a scheme ],
(I, 2.1.8), 98
— ÄV/ [ schema de base / base scheme ],
(I, 2.5.1), 100
— ÛÜ Noether V/ [ schema localement noetherien / locally noetherian scheme ],
(I, 6.1.1), 140
— ÛÜV/ [ schema local / local scheme ],
(I, 2.1.8), 98
— ÛÜ�V/ [ schema localement integre / locally integral scheme ],
(I, 2.1.8), 95
— ëÏV/ [ schema connexe / connected scheme ],
(I, 2.1.8), 95
— 3m8þ¤p��V/ [ schema induit sur un ouvert / induced scheme on an open set ],
(I, 2.1.7), 95
— �V/ [ schema integre / integral scheme ],
(I, 2.1.8), 95
V/� K �:���� (Ù¥ K ´�) [ corps des valeurs d’un point d’un schema a valeurs
dans K / value field of a point of a scheme with values in K ],
(I, 3.4.5), 110
V/�Ú [ somme de schemas / sum of schemes ],
(I, 3.1), 101
V/�AÛ: [ point geometrique d’un schema / geometric point of a scheme ],
(I, 3.4.5), 110
V/�AÛ:�ê [nombre geometrique de points d’un schema / geometric number of points
of a scheme ],
(I, 6.4.8), 149
V/�?�8BX [ systeme inductif adique de schemas / adic inductive system of schemes ],
(I, 10.12.2), 209
V/�ÛÜÓ� [ isomorphisme local de schemas / local isomorphism of schemes ],
(I, 4.5.2), 125
V/���3V/¥�:, T �: (Ù¥ T ´V/) [ point d’un schema a valeurs dans un schema
230 ¢ Ú
/ point of a scheme with values in a scheme ],
(I, 3.4.1), 109
V/���3�¥�:, B �: (Ù¥ B ´�) [ point d’un schema a valeurs dans un anneau /
point of a scheme with values in a ring ],
(I, 3.4.4), 110
V/���3ÛÜ�¥�:� ¤ [ localite d’un point d’un schema a valeurs dans un anneau
local / location of a point of a scheme with values in a local ring ],
(I, 3.4.5), 110
V/� u x ∈ X ?� K �: (Ù¥ K ´�) [ point d’un schema a valeurs dans K localise en
x ∈ X / point of a scheme with values in K located at x ∈ X ],
(I, 3.4.5), 110
V/�� [morphisme de schemas / morphism of schemes ],
(I, 2.2.1), 95
— 4�� [morphisme fermee / closed morphism ],
(I, 2.2.6), 96
— �d��� [morphismes equivalents / equivalent morphisms ],
(I, 7.1.1), 155
— é���� [morphisme diagonal / diagonal morphism ],
(I, 5.3.1), 130
— ©l�� [morphisme separe / separated morphism ],
(I, 5.4.1), 134
— 2�¹N�� [morphisme universellement injectif / universally injective morphism ],
(I, 3.5.4), 113
— Q�z�� [morphisme reduit / reduced morphism ],
(I, 5.1.5), 127
— ;b�� [morphisme radiciel / radicial morphism ],
(I, 3.5.4), 113
— ÛÜk�.�� [morphisme localement de type fini / morphism locally of finite type ],
(I, 6.6.2), 153
— m�� [morphisme ouvert / open morphism ],
(I, 2.2.6), 96
— <í5�� [morphisme dominant / dominant morphism ],
(I, 2.2.6), 96
— [;�� [morphisme quasi-compact / quasi-compact morphism ],
(I, 6.6.1), 152
— Vkn�� [morphisme birationnel / birational morphism ],
(I, 2.2.9), 97
— ���ñ- [morphisme majore par un autre / morphism bounded by another ],
(I, 4.1.8), 119
¢ Ú 231
— ���ã��� [morphisme graphe d’un morphisme / graph morphism of a morphism ],
(I, 3.3.14), 108
— N÷��� [morphisme surjectif / surjective morphism ],
(I, 2.2.6), 96
— k�.�� [morphisme de type fini / morphism of finite type ],
(I, 6.3.1), 143
V/���n� [fibre d’un morphisme de schemas / fiber of a morphism of schemes ],
(I, 3.6.2), 115
V/3��e�V� [ image schematique d’un pr’eschema par un morphisme / schematic
image of a scheme under a morphism ],
(I, 9.5.3), 179
H
ܤ [ compose / composition ],
(, )
— ψ ��� ψ′ ���ܤ [ compose d’un ψ-morphisme et d’un ψ′-morphisme / compo-
sition of a ψ-morphism and a ψ′-morphism ],
(0, 3.5.2), 22
— Ψ ��� Ψ′ ���ܤ [ compose d’un Ψ-morphisme et d’un Ψ′-morphisme / compo-
sition of a Ψ-morphism and a Ψ′-morphism ],
(0, 4.4.2), 32
� [ anneau / ring ],
(, )
— ?��, I ?�� [ anneau adique, anneau I-adique / adic ring, I-adic ring ],
(0, 7.1.9), 53
— ý?��, I ý?�� [ anneau preadique, anneau I-preadique / preadic ring, I-preadic
ring ],
(0, 7.1.9), 53
— ©ª� [ anneau de fractions / ring of fractions ],
(0, 1.2.2), 3
— Q�� [ anneau reduit / reduced ring ],
(0, 1.1.1), 3
— �N� [ anneau admissible / admissible ring ],
(0, 7.1.2), 52
— �N��½Ân� [ ideal de definition d’un anneau admissible / definition ideal of an
admissible ring ],
(0, 7.1.2), 52
— ��©ª� [ anneau complet de fractions / complete ring of fractions ],
(0, 7.6.5), 64
232 ¢ Ú
— �5ÿÀ� [ anneau linearement topologise / linearly topologized ring ],
(0, 7.1.1), 52
— ý�N� [ anneau preadmissible / preadmissible ring ],
(0, 7.1.2), 52
— �� [ anneau integre / domain or integral domain ],
(0, 1.0.6), 2
— �K� [ anneau regulier / regular ring ],
(0, 4.1.4), 28
��¦5f8 [ partie multiplicative d’un anneau / multiplicative subset of a ring ],
(0, 1.2.1), 3
— �Ú¦5f8 [ partie multiplicative saturee / saturated multiplicative subset ],
(0, 1.4.3), 6
��� [ radical d’un anneau / radical of a ring ],
(0, 1.1.2), 3
��Ì, ���Ì [ spectre d’un anneau / spectrum of a ring ],
(I, 1.1.1), 72
��m [ espace annele / ringed space ],
(0, 4.1.1), 26
— �È�m�.�m [ espace sous-jacent a un espace annele / underlying space of a ringed
space ],
(0, 4.1.1), 26
— �È�m�(�� [ faisceau structural d’un espace annele / structure sheaf of a ringed
space ],
(0, 4.1.1), 26
— �È�m�²"�� [morphisme plat d’espaces anneles / flat morphism of ringed
spaces ],
(0, 6.7.1), 51
— �È�m���, ÿÀ�È�m��� [morphisme d’espaces anneles, d’espaces topologique-
ment anneles / morphism of ringed spaces, of topologically ringed spaces ],
(0, 4.1.1), 26
— �È�m�§¢²"�� [morphisme fidelement plat d’espaces anneles / faithfully flat
morphism of ringed spaces ],
(0, 6.7.1), 52
— �È�mþ��ê5� [ faisceau algebrique sur un espace annele / algebraic sheaf over
a ringed space ],
(0, 4.1.3), 27
— ÛÜ�È�m [ espace annele en anneaux locaux / locally ringed space ],
(0, 4.1.1), 44
— ÅÜ ¤��È�m [ espace annele obtenu par recollement / ringed space obtained by
¢ Ú 233
glueing ],
(0, 4.1.7), 29
— ÿÀ�È�m [ espace topologiquement annele / topologically ringed space ],
(0, 4.1.1), 26
— 3f�mþ¤p���È�m [ espace annele induit sur un partie / induced ringed space
on a subspace ],
(0, 4.1.2), 27
— �5�È�m, Q��È�m, �K�È�m [ espace annele normal, espace annele reduit,
espace annele regulier / normal ringed space, reduced ringed space, regular ringed
space ],
(0, 4.1.4), 28
�Ó���)ÌN� [ application de spectre d’anneaux associee a un homomorphisme d’anneaux
/ map of spectra of rings associated to a ring homomorphism ],
(I, 1.2.1), 75
J
Ä�½Ân��| [ systeme fondamental d’Ideaux de definition / fundamental system of ideal
sheaves of definition ],
(I, 10.3.7 Ú 10.5.1), 187, 189
�¡3�:?��� [ valeur d’une section en un point / value of a section at a point ],
(0, 5.5.1), 44
E\ [ immersion / immersion ],
(, )
— V/�E\, 4E\, mE\ [ immersion, immersion fermee, immersion ouvert de
schemas / immersion, closed immersion, open immersion of schemes ],
(I, 4.2.1), 120
— V/�ÛÜE\ [ immersion locale de schemas / local immersion of schemes ],
(I, 4.5.1), 125
— E\��)Ó� [ isomorphisme associe a une immersion / isomorphism associated to
an immersion ],
(I, 4.2.1), 120
— E\��)fV/ [ sous-schema associe a une immersion / subscheme associated to
an immersion ],
(I, 4.2.1), 120
²LÄV/*Ü ���V/ [ schema obtenu par extension du schema de base / scheme
obtained by extension of base scheme ],
(I, 3.3.6), 106
ÛÜ� [ anneau local / local ring ],
(0, 1.0.7), 2
234 ¢ Ú
— Ó �ÛÜ� [ anneaux locaux apparentes / allied local rings ],
(I, 8.1.4), 166
— X ÷X Y �ÛÜ�, Y 3 X ¥�ÛÜ� (Ù¥ Y ´V/ X �Ø��4f8) [ anneau local
de X le long de Y , anneau local de Y dans X / local ring of X along Y , local ring
of Y in X ],
(I, 2.1.6), 94
ÛÜ��÷Þ'X [ anneau local dominant / dominating local ring ],
(I, 8.1.1), 165
ÛÜ��m�ÛÜÓ� [ homomorphisme local d’anneaux locaux / local homomorphism of
local rings ],
(0, 1.0.7), 2
K
�N��/ªÌ [ spectre formel d’un anneau admissible / formal spectrum of an admissible
ring ],
(I, 10.1.2), 183
�m [ espace / space ],
(, )
— Kolmogoroff �m [ espace de Kolmogoroff / Kolmogoroff space ],
(0, 2.1.3), 12
— Noether �m [ espace noetherien / noetherian space ],
(0, 2.2.1), 13
— Ø���m [ espace irreductible / irreducible space ],
(0, 2.1.1), 11
— ÛÜ Noether �m [ espace localement noetherien / locally noetherian space ],
(0, 2.2.1), 13
— [;�m [ espace quasi-compact / quasi-compact space ],
(0, 2.1.3), 12
L
n� [ ideal / ideal ],
(, )
— �ªn� [ ideal qui eqal a sa racine / radical ideal, ideal that equals to its radical ],
(0, 1.1.1), 2
— �N��½Ân� [ ideal de definition d’un anneau admissible / definition ideal of an
admissible ring ],
(0, 7.1.2), 52
— n��� [ racine d’un ideal / radical of an ideal ],
¢ Ú 235
(0, 1.1.1), 2
— �n� [ ideal premier / prime ideal ],
(0, 1.0.6), 2
n�� [ faisceau d’ideaux / sheaf of ideals ],
(0, 4.1.3), 27
— ½Ân�� [ faisceau d’ideaux de definition / sheaf of definition ideals ],
(I, 10.3.3 Ú 10.5.1), 186, 189
— n��¤½Â�4fV/ [ sous-schema ferme defini par un faisceau d’ideaux / closed
subscheme defined by an ideal sheaf ],
(I, 4.1.2), 118
<í S � S V/ [ S-schema dominant / dominant S-scheme ],
(I, 2.5.1), 100
M
� [module / module ],
(, )
— A ²"� [module A-plat / A-flat module ],
(0, 6.2), 46
— ©ª� [module des fractions / module of fractions ],
(0, 1.2.2), 3
— [k�� [module quasi-fini / quasi-finite module ],
(0, 7.4.1), 60
— ²"� [module plat / flat module ],
(0, 6.1.1), 46
— k�¥«� [module admet une presentation finie / module of finite presentation ],
(0, 1.0.5), 2
— §¢²"� [module fidelement plat / faithfully flat module ],
(0, 6.4.1), 48
� I �zV/ [ schema deduit par reduction mod I / scheme deduced by mod I reduction ],
(I, 3.7.1), 116
�� ϕ Ó� [ ϕ-homomorphisme de modules / ϕ-homomorphism of modules ],
(0, 1.0.2), 1
����ÜþÈ [ produit tensoriel complete de modules / complete tensor product of modules ],
(0, 7.7.1), 67
N
_� [ image reciproque / inverse image ],
(, )
236 ¢ Ú
— B ���_� [ image reciproque d’un B-Module / inverse image of an B-module ],
(0, 4.3.1), 31
— S V/�_� [ image reciproque d’un S-schema / inverse image of an S-scheme ],
(I, 3.3.6), 106
— S ���_� [ image reciproque d’un S-morphisme / inverse image of an S-morphism ],
(I, 3.3.7), 106
— ý��_� [ image reciproque d’un prefaisceau / inverse image of a presheaf ],
(0, 3.5.3), 22
— fV/�_� [ image reciproque d’un sous-schema / inverse image of a subscheme ],
(I, 4.4.1), 124
ÅÜ� [ faisceau obtenu par recollement / sheaf obtained by glueing ],
(0, 3.3.1), 19
ÅÜ�È�m [ espace annele obtenu par recollement / ringed space obtained by glueing ],
(0, 4.1.7), 29
ÅÜ^� [ condition de recollement / glueing condition ],
(0, 3.3.1 Ú 4.1.7), 18
ÅÜ^� [ condition de recollement / glueing condition ],
(0, 3.3.1 Ú 4.1.7), 29
S
��/ª�?ê [ series formelles restreintes / restricted formal power series ],
(0, 7.5.1), 61
¦�¡�"��:8 [ ensemble ou s’annule une section / set where a section is annihilated ],
(0, 5.5.1), 44
VÓ� [ di-homomorphisme / di-homomorphism ],
(0, 1.0.2), 1
^� [ image directe / direct image ],
(, )
— A ���^� [ image directe d’un A -Module / direct image of an A -module ],
(0, 4.2.1), 29
— ý��^� [ image directe d’un prefaisceau / direct image of a presheaf ],
(0, 3.4.1), 20
T
���ã� [ graphe d’un morphisme / graph of a morphism ],
(I, 5.3.11), 132
— ���ã��� [morphisme graphe d’un morphisme / graph morphism of a morphism ],
(I, 3.3.14), 108
¢ Ú 237
��3��zþ�òÿ [ prolongement d’un morphisme aux completes / extension of a mor-
phism to completions ],
(I, 10.9.1), 201
ÿÀ���m�ëYÓ� [ homomorphisme continu de faisceaux d’anneaux topologiques / con-
tinuous homomorphism of sheaves of topological rings ],
(0, 3.1.4), 15
ÿÀ�"� [ element topologiquement nilpotent / topologically nilpotent element ],
(0, 7.1.1), 52
W
��z [ complete / completion ],
(, )
— OX ��Ó�÷X4f8���z [ complete d’un homomorphisme de OX-Modules le
long d’une partie fermee / completion of a homomorphism of OX -modules along a
closed subset ],
(I, 10.8.4), 197
— OX ��÷X4f8���z [ complete d’un OX-Module le long d’une partie fermee /
completion of an OX -module along a closed subset ],
(I, 10.8.4), 197
— V/÷X4f8���z [ compete d’un schema le long d’une partie fermee / completion
of a scheme along a closed subset ],
(I, 10.8.5), 198
X
n�È [ produit fibre / fibred product ],
(, )
— S V/�n�È [ produit fibre de S-schemas / fibred product of S-schemes ],
(I, 3.2.1), 101
— S /ªV/�n�È [ produit fibre de S-schemas formels / fibred product of formal
S-schemes ],
(I, 10.7.1), 195
— 8Ü�n�È [ produit fibre d’ensembles / fibred product of sets ],
(I, 3.4.2), 109
— n�È�;�ÝK [ projections canoniques d’un produit fibre / canonical projections of
a fibred product ],
(I, 3.2.1), 101
�� [ restriction / restriction ],
(, )
238 ¢ Ú
— V/��3fV/þ��� [ restriction d’un morphisme de schemas a un sous-schema
/ restriction of a morphism of schemes onto a subscheme ],
(I, 4.1.7), 119
— V/3m8þ��� [ restriction d’un schema a un ouvert / restriction of a scheme onto
an open set ],
(I, 2.1.7), 95
— �È�m��3f�mþ��� [ restriction d’un morphisme d’espaces anneles a un
partie / restriction of a morphism of ringed spaces onto a subspace ],
(0, 4.1.2), 27
— �È�m3f�mþ��� [ restriction d’un espace annele a un partie / restriction of
a ringed space onto a subspace ],
(0, 4.1.2), 27
— knN�3m8þ���, 3m8þp��knN� [ application rationnelle induite sur
un ouvert / induced rational map on an open set ],
(I, 7.1.2), 156
/ªV/ [ schema formel / formal scheme ],
(I, 10.4.2), 187
— Noether /ªV/ [ schema formel noetherien / noetherian formal scheme ],
(I, 10.4.2), 187
— ��/ªV/ [ schema formal affine / affine formal scheme ],
(I, 10.1.2), 183
— ?�/ªV/ [ schema formel adique / adic formal scheme ],
(I, 10.4.2), 187
— ÛÜ Noether /ªV/ [ schema formel localement noetherien / locally noetherian formal
scheme ],
(I, 10.4.2), 187
/ªV/ X � OX ½Ân�� [ OX-Ideal de definition d’un schema formel X / OX -ideal of
definition of a formal scheme X ],
(I, 10.3.3 Ú 10.5.1), 186
/ªV/ X � OX ½Ân�� [ OX-Ideal de definition d’un schema formel X / OX -ideal of
definition of a formal scheme X ],
(I, 10.3.3 Ú 10.5.1), 189
/ªV/� A �� (Ù¥ A ´�N�) [ A-morphisme de schemas formels / A-morphism of
formal schemes ],
(I, 10.4.7), 188
/ªV/� S �� (Ù¥ S ´/ªV/) [ S-morphisme de schemas formels / S-morphism of
formal schemes ],
(I, 10.4.7), 188
/ªV/��� [morphisme de schemas formels / morphism of formal schemes ],
¢ Ú 239
(I, 10.4.5), 188
— /ªV/�é���� [morphisme diagonal de schemas formels / diagonal morphism
of formal schemes ],
(I, 10.15.1), 215
— /ªV/�©l�� [morphisme separe de schemas formels / separated morphism of
formal schemes ],
(I, 10.15.1), 215
— /ªV/�?��� [morphisme adique de schemas formels / adic morphism of formal
schemes ],
(I, 10.12.1), 208
— /ªV/�k�.�� [morphisme de type fini de schemas formels / morphism of finite
type of formal schemes ],
(I, 10.13.3), 211
Y
��: [ point generique / generic point ],
(0, 2.1.2), 12
Å"� [nilradical / nilradical ],
(, )
— ��Å"� [nilradical d’un anneau / nilradical of a ring ],
(0, 1.1.1), 2
— OX �ê��Å"� [Nilradical d’une OX-Algebre / nilradical of an OX -algebra ],
(I, 5.1.1), 126
kn¼ê (3V/þ) [ fonction rationnelle / rational function ],
(I, 7.1.2), 155
kn¼ê� (3V/þ) [ faisceau des fonctions rationnelles / sheaf of rational functions ],
(I, 7.3.2), 162
kn¼ê� (3V/þ) [ anneau des fonctions rationnelles / ring of rational functions ],
(I, 2.1.6 Ú 7.1.3), 95, 156
knN�, S knN� [ application rationnelle, S-application rationnelle / rational map, S-
rational map ],
(I, 7.1.2), 155
— knN��½Â� [ domaine de definition d’une application rationnelle / domain of
definition of a rational map ],
(I, 7.2.1), 159
— knN�3m8þ���, 3m8þp��knN� [ application rationnelle induite sur
un ouvert / induced rational map on an open set ],
(I, 7.1.2), 156
— knN�3�:?k½Â [ application rationnelle definie en un point / rational map
240 ¢ Ú
defined at a point ],
(I, 7.2.1), 159
— 3 Spec Ox þp��knN� [ application rationnelle induite sur Spec Ox / induced
raional map on Spec Ox ],
(I, 7.2.8), 161
ý� [ prefaisceau / presheaf ],
(, )
— K �ý�, ��3�Æ K ¥�ý� [ prefaisceau a valeurs dans une categorie K /
presheaf with values in a category K ],
(0, 3.1.2), 14
— ~�ý� [ prefaisceau constant / constant presheaf ],
(0, 3.6.1), 24
— ÿÀÄþ�ý� [ prefaisceau sur une base d’ouverts / presheaf on a base of open sets ],
(0, 3.2.1), 16
— ÿÀÄþ�ý���� [morphisme de prefaisceaux definis sur une base d’ouverts /
morphism of presheaves defined on a base of open sets ],
(0, 3.2.3), 18
— 3m8þ�c\ý� [ prefaisceau induit sur un ouvert / presheaf induced on an open
set ],
(0, 3.1.5), 15
ý�� ψ �� [ ψ-morphisme de prefaisceaux / ψ-morphism of presheaves ],
(0, 3.5.1), 21
Z
�N�¡¤½Â�Ó� [ homomorphisme defini par une section globale / homomorphism de-
fined by a global section ],
(0, 5.1.1), 35
|8 [ support / support ],
(, )
— ��|8 [ support d’un module / support of a module ],
(0, 1.7.1), 10
— +�!��!����|8 [ support d’un faisceau de groupes, de anneaux, de modules /
support of a sheaf of groups, of rings, of modules ],
(0, 3.1.6), 16
� [ rang / rank ],
(, )
— k� K V/�� [ rang d’un K-schema fini / rank of a finite K-scheme ],
(I, 6.4.5), 148
— k� K V/��©� [ rang separable d’un K-schema fini / separable rank of a finite
¢ Ú 241
K-scheme ],
(I, 6.4.8), 149
— ÃL OX ������ (Ù¥ X ´�V/) [ rang generique d’un OX-Module sans torsion
/ generic rank of a torsion-free OX -module ],
(I, 7.4.2), 164
— ÛÜgd OX ���� [ rang d’un OX-Module localement libre / rank of a locally free
OX -module ],
(0, 5.4.1), 39
fV/ [ sous-schema / subscheme ],
(I, 4.1.3), 118
— 4fV/ [ sous-schema ferme / closed subscheme ],
(I, 4.1.3), 118
— E\��)fV/ [ sous-schema associe a une immersion / subscheme associated to
an immersion ],
(I, 4.2.1), 120
— n��¤½Â�4fV/ [ sous-schema ferme defini par un faisceau d’ideaux / closed
subscheme defined by an ideal sheaf ],
(I, 4.1.2), 118
— mfV/ [ sous-schema ouvert / open subscheme ],
(I, 4.1.5), 119
fV/�V4� [ adherence schematique d’un sous-schema / schematic closure of a sub-
scheme ],
(I, 9.5.11), 181
f���;�òÿ [ prolongement canonique d’un sous-Module / canonical extension of a
subsheaf of modules ],
(I, 9.4.1), 176
