Dieudonne

Dieudonne

By LucBusiness Non-Profit

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Dieudonne episodes

September 06, 2023 P50. Def projective space.
Xi=Spec A[Ti^-1T_j]j
3 min
September 06, 2023 P51. Def B_(f)
D+(f) homeo to Spec B_(f)
3 min
September 06, 2023 P51. Let f in B be a homogeneous element. D+(f) constitute a base.
D+(f) = ProjB \ V+ (fB). The open sets of this form are called principal open sets. They constitute a base of open sets of Proj B. In fact, we can restrict ourselves to the open sets D+ (f)
2 min
September 06, 2023 Lemma 3.35 projB
Not containing B+; intersecting with B+ is contained in radical.
5 min
September 05, 2023 Lemma 3.23 morphism to affine; k-rational pts are those k(x)=k.
Z(I) bijective to k-rational points of Spec k[…]/I
15 min
September 05, 2023 prop. 3.20 closed immersion into affine is affine Spec A/I
Morphisme into affine?
4 min
September 05, 2023 Lemma 3.17 closed immersion from A to A/I; spec k(x) to X map to x;
Def 3.19 closed sub scheme
10 min
September 05, 2023 Def 3.13 map of schemes Prop 3.14 ring maps gives scheme maps
Spec O_X,x to X.
8 min
September 05, 2023 Prop 3.12 X_f is open subset with O_X(X_f) iso O_X(X)_f
Condition 3.2 is needed.
7 min
September 05, 2023 Lemma 3.7 D(g) of affine is affine
Prop3.9 Open of scheme is scheme. Open sub scheme; affine open subset.
7 min

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