algebra-geometric correpondence for real or complex manifolds

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Is it true that for either complex or real differentiable manifolds, the space of points of the manifolds corresponds to the maximal (or prime) spectrum of the ring of functions (holomorphic functions in the complex case, real-valued differentiable functions in the real case) on the manifold? I'm curious how similar to algebraic geometry these cases are.




differential-geometry algebraic-geometry complex-geometry




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  • math.stackexchange.com/questions/1406035/… and math.stackexchange.com/questions/226736/… may be useful. Briefly, the maximal spectrum of the ring of continuous real-valued functions on a compact Hausdorff space is naturally homeomorphic to the space. For complex-analytic manifolds, the only chance for any homeomorphism is if your manifold is Stein, but I do not know the answer in this case.
    – KReiser
    Aug 1 at 4:24















up vote
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Is it true that for either complex or real differentiable manifolds, the space of points of the manifolds corresponds to the maximal (or prime) spectrum of the ring of functions (holomorphic functions in the complex case, real-valued differentiable functions in the real case) on the manifold? I'm curious how similar to algebraic geometry these cases are.




differential-geometry algebraic-geometry complex-geometry




share|cite|improve this question





















  • math.stackexchange.com/questions/1406035/… and math.stackexchange.com/questions/226736/… may be useful. Briefly, the maximal spectrum of the ring of continuous real-valued functions on a compact Hausdorff space is naturally homeomorphic to the space. For complex-analytic manifolds, the only chance for any homeomorphism is if your manifold is Stein, but I do not know the answer in this case.
    – KReiser
    Aug 1 at 4:24













up vote
1
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up vote
1
down vote

favorite











Is it true that for either complex or real differentiable manifolds, the space of points of the manifolds corresponds to the maximal (or prime) spectrum of the ring of functions (holomorphic functions in the complex case, real-valued differentiable functions in the real case) on the manifold? I'm curious how similar to algebraic geometry these cases are.




differential-geometry algebraic-geometry complex-geometry




share|cite|improve this question













Is it true that for either complex or real differentiable manifolds, the space of points of the manifolds corresponds to the maximal (or prime) spectrum of the ring of functions (holomorphic functions in the complex case, real-valued differentiable functions in the real case) on the manifold? I'm curious how similar to algebraic geometry these cases are.





differential-geometry algebraic-geometry complex-geometry





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 1 at 4:13









KReiser

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7,44011230









asked Aug 1 at 3:59









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562413











  • math.stackexchange.com/questions/1406035/… and math.stackexchange.com/questions/226736/… may be useful. Briefly, the maximal spectrum of the ring of continuous real-valued functions on a compact Hausdorff space is naturally homeomorphic to the space. For complex-analytic manifolds, the only chance for any homeomorphism is if your manifold is Stein, but I do not know the answer in this case.
    – KReiser
    Aug 1 at 4:24

















  • math.stackexchange.com/questions/1406035/… and math.stackexchange.com/questions/226736/… may be useful. Briefly, the maximal spectrum of the ring of continuous real-valued functions on a compact Hausdorff space is naturally homeomorphic to the space. For complex-analytic manifolds, the only chance for any homeomorphism is if your manifold is Stein, but I do not know the answer in this case.
    – KReiser
    Aug 1 at 4:24
















math.stackexchange.com/questions/1406035/… and math.stackexchange.com/questions/226736/… may be useful. Briefly, the maximal spectrum of the ring of continuous real-valued functions on a compact Hausdorff space is naturally homeomorphic to the space. For complex-analytic manifolds, the only chance for any homeomorphism is if your manifold is Stein, but I do not know the answer in this case.
– KReiser
Aug 1 at 4:24





math.stackexchange.com/questions/1406035/… and math.stackexchange.com/questions/226736/… may be useful. Briefly, the maximal spectrum of the ring of continuous real-valued functions on a compact Hausdorff space is naturally homeomorphic to the space. For complex-analytic manifolds, the only chance for any homeomorphism is if your manifold is Stein, but I do not know the answer in this case.
– KReiser
Aug 1 at 4:24
















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