Krull dimension of the ring of global sectionsInjective dimension of $mathcalO_X$-modulesKrull dimension and Morley rankDo constructible sets have Krull dimension?Compare global sections of restriction and pullback of sheavesKrull-dimension of local domainCan the transcendence degree differ from the Krull dimension for the pluricanonical ring of a variety?Schemes monomorphing into affine scheme of dimension 1Irreducible of finite Krull dimension implies quasi-compact?Finiteness of Krull dimension is localClosed points on scheme locally of finite Krull dimension
Krull dimension of the ring of global sections
Injective dimension of $mathcalO_X$-modulesKrull dimension and Morley rankDo constructible sets have Krull dimension?Compare global sections of restriction and pullback of sheavesKrull-dimension of local domainCan the transcendence degree differ from the Krull dimension for the pluricanonical ring of a variety?Schemes monomorphing into affine scheme of dimension 1Irreducible of finite Krull dimension implies quasi-compact?Finiteness of Krull dimension is localClosed points on scheme locally of finite Krull dimension
2
$begingroup$
Let $X$ be an irreducible scheme. Can the Krull dimension of $mathcalO_X(X)$ exceed that of $X$?
ag.algebraic-geometry schemes
asked 3 hours ago
Anna KarelinaAnna Karelina
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2
$begingroup$
Let $X$ be an irreducible scheme. Can the Krull dimension of $mathcalO_X(X)$ exceed that of $X$?
ag.algebraic-geometry schemes
asked 3 hours ago
Anna KarelinaAnna Karelina
111
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Anna Karelina is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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2
2
2
$begingroup$
Let $X$ be an irreducible scheme. Can the Krull dimension of $mathcalO_X(X)$ exceed that of $X$?
ag.algebraic-geometry schemes
asked 3 hours ago
Anna KarelinaAnna Karelina
111
New contributor
Anna Karelina is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Let $X$ be an irreducible scheme. Can the Krull dimension of $mathcalO_X(X)$ exceed that of $X$?
ag.algebraic-geometry schemes
ag.algebraic-geometry schemes
asked 3 hours ago
Anna KarelinaAnna Karelina
111
New contributor
Anna Karelina is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 3 hours ago
Anna KarelinaAnna Karelina
111
New contributor
Anna Karelina is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 3 hours ago
Anna KarelinaAnna Karelina
111
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Anna Karelina is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 3 hours ago
Anna KarelinaAnna Karelina
111
asked 3 hours ago
Anna KarelinaAnna Karelina
111
111
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Anna Karelina is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1 Answer
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Yes, this happens if $X$ is the punctured spectrum of a two dimensional regular local ring.
answered 2 hours ago
darxdarx
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what is the Krull dimension of such $X$? I believe $X$ has closed points, so puncturing should not really change anything, right?
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– schematic_boi
2 hours ago
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3
$begingroup$
Yes, this happens if $X$ is the punctured spectrum of a two dimensional regular local ring.
answered 2 hours ago
darxdarx
311
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what is the Krull dimension of such $X$? I believe $X$ has closed points, so puncturing should not really change anything, right?
$endgroup$
– schematic_boi
2 hours ago
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3
$begingroup$
Yes, this happens if $X$ is the punctured spectrum of a two dimensional regular local ring.
answered 2 hours ago
darxdarx
311
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darx is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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what is the Krull dimension of such $X$? I believe $X$ has closed points, so puncturing should not really change anything, right?
$endgroup$
– schematic_boi
2 hours ago
add a comment |
3
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$begingroup$
Yes, this happens if $X$ is the punctured spectrum of a two dimensional regular local ring.
answered 2 hours ago
darxdarx
311
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darx is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$
Yes, this happens if $X$ is the punctured spectrum of a two dimensional regular local ring.
answered 2 hours ago
darxdarx
311
New contributor
darx is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 hours ago
darxdarx
311
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answered 2 hours ago
darxdarx
311
answered 2 hours ago
darxdarx
311
311
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New contributor
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$begingroup$
what is the Krull dimension of such $X$? I believe $X$ has closed points, so puncturing should not really change anything, right?
$endgroup$
– schematic_boi
2 hours ago
add a comment |
$begingroup$
what is the Krull dimension of such $X$? I believe $X$ has closed points, so puncturing should not really change anything, right?
$endgroup$
– schematic_boi
2 hours ago
$begingroup$
what is the Krull dimension of such $X$? I believe $X$ has closed points, so puncturing should not really change anything, right?
$endgroup$
– schematic_boi
2 hours ago
$begingroup$
what is the Krull dimension of such $X$? I believe $X$ has closed points, so puncturing should not really change anything, right?
$endgroup$
– schematic_boi
2 hours ago
add a comment |
Anna Karelina is a new contributor. Be nice, and check out our Code of Conduct.
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