Question

On the informal interpretation of the scheme-theoretic image

score 40 · Answer 1 · 2026-04-01 20:02:28

40

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On the informal interpretation of the scheme-theoretic image

Published on 01 Apr 2026 - 20:02

score 43 · Answer 2 · 2023-12-02 20:05:30

43

Views

Affine line over an arbitrary scheme

Published on 02 Dec 2023 - 20:05

score 61 · Answer 3 · 2026-03-25 20:20:49

61

Views

If $f:\operatorname{Spec} R \to X$ is a map with $R$ local and with closed point landing in an open $U\subset X$, then $im(f)\subset U$ too.

Published on 25 Mar 2026 - 20:20

score 64 · Answer 4 · 2026-03-25 20:20:49

64

Views

If $R$ is a local ring, the morphism of schemes $f: \operatorname{Spec} R \to X$ is determined by the image of the closed point?

Published on 25 Mar 2026 - 20:20

score 81 · Answer 5 · 2026-02-23 18:41:45

81

Views

Open immersion of schemes and pullbacks

Published on 23 Feb 2026 - 18:41

score 41 · Answer 6 · 2026-03-29 12:11:22

41

Views

$X$ a scheme, $\mathfrak{p} \in \operatorname{Spec}(A) \subset X$. Then $Im(\phi: A\rightarrow A_{\mathfrak{p}})\subset D(f)$, $f\in A/\mathfrak{p}$

Published on 29 Mar 2026 - 12:11

score 107 · Answer 7 · 2023-12-10 08:58:39

107

Views

Why is $Im(f\times_k g)=p_1^{-1}(Imf)\cap p_2^{-1}(Img)$?

Published on 10 Dec 2023 - 8:58

score 106 · Answer 8 · 2023-12-10 20:01:07

106

Views

Calculating the fiber of the morphism of schemes $f:\operatorname{Spec} k[T,U]/(TU-1) \rightarrow \operatorname{Spec} k[T]$

Published on 10 Dec 2023 - 20:01

score 49 · Answer 9 · 2023-12-10 21:45:01

49

Views

Is every morphism of $K$-schemes a $K$-morphism?

Published on 10 Dec 2023 - 21:45

score 53 · Answer 10 · 2023-12-12 20:32:00

53

Views

On the notion of generic fiber

Published on 12 Dec 2023 - 20:32

score 91 · Answer 11 · 2026-03-26 16:05:25

91

Views

Show the problem of flat base change is local on the source and target

Published on 26 Mar 2026 - 16:05

score 58 · Answer 12 · 2026-02-23 07:02:29

58

Views

If $\mathfrak{p}_y$ the preimage of $\mathfrak{m}_x$ by $\mathcal{O}_Y(Y)\rightarrow\mathcal{O}_X(X)\rightarrow \mathcal{O}_{X,x}$, show that $f(x)=y$

Published on 23 Feb 2026 - 7:02

score 93 · Answer 13 · 2026-03-25 23:09:30

93

Views

The Splitting Principle for Varieties

Published on 25 Mar 2026 - 23:09

score 154 · Answer 14 · 2026-04-01 21:32:48

154

Views

Is a finitely generated and globally generated $\mathcal{O}_X$-module over non-quasicompact $X$ always not finitely globally generated?

Published on 01 Apr 2026 - 21:32

score 49 · Answer 15 · 2023-12-26 09:19:25

49

Views

Locally closed point in locally noetherian scheme

Published on 26 Dec 2023 - 9:19

List Question

On the informal interpretation of the scheme-theoretic image

Affine line over an arbitrary scheme

If $f:\operatorname{Spec} R \to X$ is a map with $R$ local and with closed point landing in an open $U\subset X$, then $im(f)\subset U$ too.

If $R$ is a local ring, the morphism of schemes $f: \operatorname{Spec} R \to X$ is determined by the image of the closed point?

Open immersion of schemes and pullbacks

$X$ a scheme, $\mathfrak{p} \in \operatorname{Spec}(A) \subset X$. Then $Im(\phi: A\rightarrow A_{\mathfrak{p}})\subset D(f)$, $f\in A/\mathfrak{p}$

Why is $Im(f\times_k g)=p_1^{-1}(Imf)\cap p_2^{-1}(Img)$?

Calculating the fiber of the morphism of schemes $f:\operatorname{Spec} k[T,U]/(TU-1) \rightarrow \operatorname{Spec} k[T]$

Is every morphism of $K$-schemes a $K$-morphism?

On the notion of generic fiber

Show the problem of flat base change is local on the source and target

If $\mathfrak{p}_y$ the preimage of $\mathfrak{m}_x$ by $\mathcal{O}_Y(Y)\rightarrow\mathcal{O}_X(X)\rightarrow \mathcal{O}_{X,x}$, show that $f(x)=y$

The Splitting Principle for Varieties

Is a finitely generated and globally generated $\mathcal{O}_X$-module over non-quasicompact $X$ always not finitely globally generated?

Locally closed point in locally noetherian scheme

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