Question

Is there a scheme $X$ , $f \in \Gamma(X;\mathcal{O}_X)$ s.t. $\Gamma(X;\mathcal{O}_X)_f \to \Gamma(X_f ;\mathcal{O}_{X_f} )$ is not an equality?

score 92 · Answer 1 · 2026-03-26 01:12:12

92

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Is there a scheme $X$ , $f \in \Gamma(X;\mathcal{O}_X)$ s.t. $\Gamma(X;\mathcal{O}_X)_f \to \Gamma(X_f ;\mathcal{O}_{X_f} )$ is not an equality?

Published on 26 Mar 2026 - 1:12

score 165 · Answer 2 · 2026-03-25 23:37:03

165

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Exercise 2.3.1 in Qing Liu's book

Published on 25 Mar 2026 - 23:37

score 148 · Answer 3 · 2020-04-07 17:14:19

148

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Do closed points of a variety lie in a codimension $1$ subvariety?

Published on 07 Apr 2020 - 17:14

score 435 · Answer 4 · 2026-03-26 01:01:10

435

Views

Affine charts for projective scheme

Published on 26 Mar 2026 - 1:01

score 46 · Answer 5 · 2026-03-29 13:41:13

46

Views

Is a conic rationally equivalent to $2L$ for $L$ a line?

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score 177 · Answer 6 · 2026-03-29 15:16:38

177

Views

Chern character of $\mathrm{ch}(i_* \mathcal{O}_L)$ for $i: L \hookrightarrow X$ a line

Published on 29 Mar 2026 - 15:16

score 241 · Answer 7 · 2020-04-10 16:19:28

241

Views

Understanding the proof of Hartshorne Prop. II.7.13.b

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score 496 · Answer 8 · 2026-03-25 23:39:08

496

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score 657 · Answer 9 · 2020-04-16 04:28:25

657

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139

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restriction of affine schemes morphisms

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score 52 · Answer 11 · 2026-03-25 23:37:59

52

Views

Schematic fiber of $\mathbb{C}^2/\mu_2$ at $0$

Published on 25 Mar 2026 - 23:37

score 1.8k · Answer 12 · 2026-03-25 23:38:06

1.8k

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score 215 · Answer 13 · 2020-04-19 16:24:19

215

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score 617 · Answer 14 · 2026-03-25 14:30:42

617

Views

Example of a $\mathbb{Q}$-Cartier divisor

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score 265 · Answer 15 · 2026-03-29 23:48:14

265

Views

The tilde construction of a finitely generated $\Gamma(X,\mathcal{O}_{X})$-module.

Published on 29 Mar 2026 - 23:48

List Question

Is there a scheme $X$ , $f \in \Gamma(X;\mathcal{O}_X)$ s.t. $\Gamma(X;\mathcal{O}_X)_f \to \Gamma(X_f ;\mathcal{O}_{X_f} )$ is not an equality?

Exercise 2.3.1 in Qing Liu's book

Do closed points of a variety lie in a codimension $1$ subvariety?

Affine charts for projective scheme

Is a conic rationally equivalent to $2L$ for $L$ a line?

Chern character of $\mathrm{ch}(i_* \mathcal{O}_L)$ for $i: L \hookrightarrow X$ a line

Understanding the proof of Hartshorne Prop. II.7.13.b

Dimension of fibers of scheme over $\mathbb{Z}$

Question about when a projection from a fiber product is open

restriction of affine schemes morphisms

Schematic fiber of $\mathbb{C}^2/\mu_2$ at $0$

A possible proof that the affine line with double origin is not affine

Morphism of k-schemes

Example of a $\mathbb{Q}$-Cartier divisor

The tilde construction of a finitely generated $\Gamma(X,\mathcal{O}_{X})$-module.

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