All Questions
Tagged with schemes gn.general-topology
13 questions with no upvoted or accepted answers
7
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433
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Ever seen a ringed group?
A locally ringed space is a common generalization of schemes and various manifolds. I am wondering about a locally ringed group which should be a common generalization of group schemes and various Lie ...
4
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0
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317
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Is the "naive" version of Chevalley's theorem still true?
Reposting from math.se in case more people are interested here.
Chevalley's theorem says that if $f \colon X \to Y$ is a morphism of finite presentation of schemes and $C \subset X$ is constructible, ...
4
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0
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483
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A slightly canonical way to associate a scheme to a Noetherian spectral space
Let $C$ be the category whose objects are Noetherian spectral topological spaces and whose morphisms are homeomorphisms. Let $\mathrm{AffSch}$ be the category of Noetherian affine schemes (morphisms ...
3
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0
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197
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Topological properties of Noetherian affine schemes that do not hold for general Noetherian spectral spaces
I used to think that the only reason why an affine scheme with a Noetherian space can fail to be Noetherian is nilpotents. It turns out that this is not true.
This leads me to the following question: ...
2
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0
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215
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A closed point in the closure of any point in the closure of any point of an irreducible scheme
Let $X$ be the underlying space of an irreducible scheme. In particular, $X$ is non-empty.
Note that the closure of any point is a closed irreducible subset. We say that a point has codimension $n$ ...
2
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0
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217
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Constructible sets, I (Morphisms)
I have a number of questions on constructible sets. The first one is on morphisms: suppose $X$ and $Y$ are constructible sets, respectively in projective spaces $\mathbf{P}_1$ and $\mathbf{P}_2$ over ...
1
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0
answers
92
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Topological space modeled by special topological structures
Let $X$ be a topological space. Suppose it is "modeled by" topological spaces of the form $\text{Spec}(A)$ for some commutative ring $A$, then, (along with some other conditions/structure), we call $...
1
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0
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298
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Fully faithful functor from schemes to spaces
Is there a fully faithful functor from the category of schemes
to the category of topological spaces and continuous maps (or some other sufficiently topological objects, e.g. smooth manifolds and ...
1
vote
0
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127
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Explicit description of the scheme obtained by relative gluing data over a base scheme
I have recently been trying to get a better understanding of the projective space bundle of a quasi-coherent sheaf of graded algebras over a scheme $X$. The key idea is the following construction ...
0
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0
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144
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Making a quasi-compact open into an affine open
Let $X$ be a spectral topological space, $U\subset X$ be a quasi-compact open subspace. Is there necessarily some scheme structure on $X$ (we do not require it to be affine) such that $U$ endowed with ...
0
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0
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146
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A scheme whose underlying space is the product of the underlying spaces of schemes
We know that the product of two spectral topological spaces is spectral.
If $X$ is the underlying space of the scheme $\mathrm{Spec}\,\mathbb{Z}[x]$, what is a simple example of an affine scheme ...
0
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325
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Grothendieck topology on a scheme equivalent to the circle
Suppose a class of morphisms of schemes is reasonable enough so that we can associate a small site to any scheme (just like small étale site). Is there a simple class of morphisms such that there is a ...
0
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0
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238
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Pro-constructible subset of scheme intersects very dense subsets?
Let $X$ be a scheme, let $D$ be a very dense subset of $X$ and let $Y$ be a pro-constructible subset of $X$. Is it true that $Y \cap D \neq \emptyset$?
If $Y$ is just constructible, this is true.
...