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Apr
16
awarded  Notable Question
Mar
25
awarded  Necromancer
Mar
2
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?
added 2 characters in body
Feb
24
revised Classical algebraic geometry in infinite dimensions?
added 896 characters in body
Feb
24
revised Classical algebraic geometry in infinite dimensions?
added 896 characters in body
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
added 3 characters in body
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 $0$.
Feb
20
asked Functions on reduced schemes are determined by their values at each point.
Feb
20
comment Irreducible closed subsets of a scheme corresponds to points
I worked out the answer, thank you. It is not as trivial as it looks.
Feb
20
accepted Irreducible closed subsets of a scheme corresponds to points
Feb
19
revised Irreducible closed subsets of a scheme corresponds to points
deleted 111 characters in body
Feb
19
asked Irreducible closed subsets of a scheme corresponds to points
Feb
19
answered Locally closed irreducible subset of an affine scheme.