List questions from affine-schemes

Published on 10 Jun 2021 - 1:00

125

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Is a pure coherent sheaf locally pure?

Published on 26 Mar 2026 - 23:09

658

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Definition of the structure sheaf on $\text{Spec} A$

Published on 25 Jun 2021 - 11:36

148

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Can we define $\operatorname{Spec}(H^0(X, \mathcal O_X))$ for a scheme $X$?

Published on 27 Jun 2021 - 15:23

237

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How to prove the Frobenius induces a homeomorphism?

Published on 03 Jul 2021 - 12:53

67

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Inclusion of open affines implies injection of coordinate rings?

Published on 06 Jul 2021 - 15:56

415

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Proving a surjective k-algebra homomorphism to be an isomorphism

Published on 27 Jul 2021 - 22:27

117

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Understanding the morphism of schemes involving nilpotents induced by: $\mathbb C[x] \to \mathbb C[x]/(x^2)$ where $x \mapsto ax \pmod {x^2}$

Published on 06 Aug 2021 - 19:12

360

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Induced morphism between affine schemes is injective

Published on 07 Aug 2021 - 15:28

172

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Example of a non-affine scheme whose reduction is affine

Published on 16 Aug 2021 - 17:39

153

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Exercise 8.1.H from Vakil's FOAG: criterion for ideals in affine open sets defining closed subscheme

Published on 18 Aug 2021 - 6:42

78

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Open subsets of affine schemes (refined question)

Published on 03 Sep 2021 - 13:15

314

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Quasi-coherent sheaves of algebras over affine scheme

Published on 18 Sep 2021 - 15:07

296

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Proving that the disjoint union of two affine schemes is isomorphic to an affine scheme

Published on 18 Sep 2021 - 21:06

230

Views

Structure sheaf of $\operatorname{Spec} A$ with $A$ an integral domain

Published on 23 Sep 2021 - 21:47

List Question

How to get such a scheme?

Is a pure coherent sheaf locally pure?

Definition of the structure sheaf on $\text{Spec} A$

Can we define $\operatorname{Spec}(H^0(X, \mathcal O_X))$ for a scheme $X$?

How to prove the Frobenius induces a homeomorphism?

Inclusion of open affines implies injection of coordinate rings?

Proving a surjective k-algebra homomorphism to be an isomorphism

Understanding the morphism of schemes involving nilpotents induced by: $\mathbb C[x] \to \mathbb C[x]/(x^2)$ where $x \mapsto ax \pmod {x^2}$

Induced morphism between affine schemes is injective

Example of a non-affine scheme whose reduction is affine

Exercise 8.1.H from Vakil's FOAG: criterion for ideals in affine open sets defining closed subscheme

Open subsets of affine schemes (refined question)

Quasi-coherent sheaves of algebras over affine scheme

Proving that the disjoint union of two affine schemes is isomorphic to an affine scheme

Structure sheaf of $\operatorname{Spec} A$ with $A$ an integral domain

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