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Sunday, October 24, 2010
Definition of ω map
Sch.5
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U⊂V⊂X and t(U^c)^c⊂t(V^c)^c⊂t(X) 3D comm.diagram
Speck-structure on t(U^c)^c (take 2)
Inverse morphism of ringed spaces
X->t(X) being a functor
3D comm. diagram involving t(X), t(U), t(U^c)^c, U
Γ(t(U))=Γ(t(U^c)^c)
t(U), t(X), t(U^c)^c commuting diagram
U, t(U), and t(U^c)^c commuting diagram
How X->Y induces t(X)->t(Y)
Hom(V,W)<->Hom(O(W),O(V)), W,V varieties, W affine
Spec k - structure of t(U^c)^c for affine U⊂V
Speck - scheme structure of t(V)', V affine variety
If V is affine variety, t(V) is an affine scheme
(x^-1A)/A=A/xA
Domain Topology
V->W induces t(V)->t(W), any varieties V,W
Global section of t(V)->Spec k gives the canonica...
The morphism of γ : t(U^c)^c->t(U) and its global ...
Compatibility of t(V)-Spec k with restrictions to ...
t(f) morphism definitioin
Spec k - structure of SpecA(V)
Spec k - structure of t(V) for general V
Spec k - structure of t(V) for affine V
Compatibility of Γ(Hom(SpecA,SpecB)) and Hom(A,B)
Spec k - structure of the iso between SpecA(V) and...
ω map for t(V)
Definition of ω map
V,t(V),SpecA(V) comm diag, scheme version
Hom(V,W) <-> Hom(A(W),A(v)), A a domain
Gluing morphisms (2)
Hom(X,Y)<->Hom(Γ(Y),Γ(X)), Y affine scheme
Global section functor
Equivalence of category: affine schemes, rings
(t(U),O)=(t(U^c)^c,F|)
t(Y^c)=t(Y)^c
α map revisited
Hom(A,G(X)) <-> Hom(X,SpecA)
α: X -> t(X)
Gluing morphisms
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