Géométrie Algébrique 2 Table des matières

V(F)

S
X→S
X S
X S
SF OS
S T FTOTFT
F1, F2: (SSch)◦→Ens S T
F1(T) = Γ(T, FT)
F2(T) = Γ(T, (FT)∨)
F1F
F2V(F)
V(F)V(F)FV(F)

X
(Ui)i∈I
q
i∈IUi−→ X.
UiX
X UiUij Uji Ui∩Uj
UiUjϕij :
Uij →Uji X
Ui∩Uj∩Uk
Uii∈I
Uij j∈I ϕij :Uij →Uji i, j, k
ϕij(Uij ∩Uik) = Uji ∩Ujk ϕik =ϕjk ◦ϕij Uij ∩Uik
qUixi∼xjxj=
ϕij(xi)xi∈Uij xj∈Uji X=qUi/∼
Ui(Uij, ϕij)
P
P
X(Ui)X
X P
UiP
Q
Q
f:X→Y(Ui)X
f Q
Ui→X→Y Q

Q
f:X→Y(Vi)X
f Q
X×YVi→ViQ
X×YVi→Vif|f−1(Vi):
f−1(Vi)→ViQ
ViY i
Uij f−1(Vi)Uij →ViQ
X x, y ∈X
x∈ {y}x y y x
x y
X
Y={y}Y
y y 7→ {y}
X X
Y
x∈XSpec(OX,x)→X
Spec(OX,x)x U x
x U U = Spec(A)
pxx y ∈U{y}=V(py)
x∈ {y}py⊂pxx
px
Apx=OX,x
X X
X= Spec(A)
D(f) = Spec(A[1/f])
X
B B
FU∈B
F B U⊂X
U Ui∈B si∈F(Ui)
i, j V ⊂Ui∩UjBsi|V=sj|V
s∈F(U)s|Ui=siiB
X
FUF(U) = lim
←−V⊂U,V ∈BF(V)
B