Sch.5 (Affine)
Sch.6 (Any variety)
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2010
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October
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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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October
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