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answered The A-valued points on a scheme
Mar
1
comment How to see $\Gamma(\mathscr{O}_S,\operatorname{Proj} S)$ as a ring?
I wanted to find a natural structure morphism $A\to \Gamma(\mathscr{O}_S,\operatorname{Proj} S)$, so perhaps I can show that the maps $A\to \Gamma(\mathscr{O}_S,D(f))$ are compatible thus lifts to a morphism $A\to \Gamma(\mathscr{O}_S,\operatorname{Proj} S)$. In this way I could create the map while avoiding the specific structure of $\Gamma(\mathscr{O}_S,\operatorname{Proj} S)$. And that gives me a morphism $\operatorname{Proj}S\to \operatorname{Spec} A$. Is it correct?
Mar
1
asked How to see $\Gamma(\mathscr{O}_S,\operatorname{Proj} S)$ as a ring?
Feb
24
revised Classical algebraic geometry in infinite dimensions?
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Feb
24
revised Classical algebraic geometry in infinite dimensions?
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Feb
24
revised Classical algebraic geometry in infinite dimensions?
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Feb
24
asked Classical algebraic geometry in infinite dimensions?
Feb
23
comment The support and the non-vanishing set of a function on a scheme
@GeorgesElencwajg So you are suggesting that in the affine case $NV(f) = D(f) = \{P\in X: f\not\in P\}$?
Feb
22
revised The support and the non-vanishing set of a function on a scheme
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Feb
22
asked The support and the non-vanishing set of a function on a scheme
Feb
20
asked CW approximation as an adjoint equivalence?
Feb
20
comment Functions on reduced schemes are determined by their values at each point.
@KReiser Haha I see now. In the affine case the image of $a$ lies in the maximal ideal $\mathfrak{m}_p$ means exactly $a\in p$, and the intersection of all primes is the nilradical. Therefore $a = 0$. Now a scheme is covered by affine opens, by the unique gluing property of sheaves, $a = 0\in\mathscr{O}_X(X)$ since its image in every affine open is $0$.