Question

$\pi:\Bbb P^1_k\to \text{Spec}(k)$ then is $\Bbb L\pi^*\tilde{k}\cong \mathcal{O}_{\Bbb P^1_k}[0]$?

score 56 · Answer 1 · 2026-03-26 09:58:07

56

Views

$\pi:\Bbb P^1_k\to \text{Spec}(k)$ then is $\Bbb L\pi^*\tilde{k}\cong \mathcal{O}_{\Bbb P^1_k}[0]$?

Published on 26 Mar 2026 - 9:58

score 195 · Answer 2 · 2026-03-25 16:08:34

195

Views

Non zero global section of line bundle and its dual $\implies \mathcal L\cong O_X$

Published on 25 Mar 2026 - 16:08

score 67 · Answer 3 · 2026-02-23 06:53:03

67

Views

When can $\textbf{SpecMax}(R)$ be a scheme?

Published on 23 Feb 2026 - 6:53

score 42 · Answer 4 · 2026-03-25 14:34:34

42

Views

Zeros of a finite support function on elliptic curve are torsion

Published on 25 Mar 2026 - 14:34

score 86 · Answer 5 · 2026-03-26 17:51:55

86

Views

Rising Sea exercise 5.3.H

Published on 26 Mar 2026 - 17:51

score 24 · Answer 6 · 2026-03-25 13:57:04

24

Views

Example of a family of ample divisors $\{A_m\}_{m\geq 1}$ on a smooth projective variety $X$ such that $mA_m$ has a basepoint?

Published on 25 Mar 2026 - 13:57

score 41 · Answer 7 · 2026-03-25 13:59:43

41

Views

global section of a B-scheme defines a morphism to projective $B$-scheme

Published on 25 Mar 2026 - 13:59

score 122 · Answer 8 · 2026-03-25 04:40:24

122

Views

An algebraic stack as a non-linear analog of a complex of vector spaces

Published on 25 Mar 2026 - 4:40

score 50 · Answer 9 · 2026-03-25 23:37:38

50

Views

A property of invertible sheaves

Published on 25 Mar 2026 - 23:37

score 65 · Answer 10 · 2026-03-25 13:58:07

65

Views

Problem showing the saturation map of a graded ring f.g. in degree 1 induces an isomorphism of projective schemes and O(1) (The Rising Sea 15.6.G)

Published on 25 Mar 2026 - 13:58

score 44 · Answer 11 · 2023-10-26 12:21:31

44

Views

Equivalent definition of "regularly immersed closed subscheme" (locally Noetherian case)

Published on 26 Oct 2023 - 12:21

score 50 · Answer 12 · 2026-03-25 19:04:39

50

Views

Prestack of coherent sheaves

Published on 25 Mar 2026 - 19:04

score 53 · Answer 13 · 2026-03-26 02:56:00

53

Views

Geometry of the discriminant locus of a morphism between varieties

Published on 26 Mar 2026 - 2:56

score 98 · Answer 14 · 2026-02-23 09:13:23

98

Views

What means “top exterior power of the sheaf of differentials $\Omega^1_{X/Y}$” when the rank of $\Omega^1_{X/Y}$ is globally unbounded?

Published on 23 Feb 2026 - 9:13

score 89 · Answer 15 · 2023-11-01 14:30:04

89

Views

Noetherian induction application

Published on 01 Nov 2023 - 14:30

List Question

$\pi:\Bbb P^1_k\to \text{Spec}(k)$ then is $\Bbb L\pi^*\tilde{k}\cong \mathcal{O}_{\Bbb P^1_k}[0]$?

Non zero global section of line bundle and its dual $\implies \mathcal L\cong O_X$

When can $\textbf{SpecMax}(R)$ be a scheme?

Zeros of a finite support function on elliptic curve are torsion

Rising Sea exercise 5.3.H

Example of a family of ample divisors $\{A_m\}_{m\geq 1}$ on a smooth projective variety $X$ such that $mA_m$ has a basepoint?

global section of a B-scheme defines a morphism to projective $B$-scheme

An algebraic stack as a non-linear analog of a complex of vector spaces

A property of invertible sheaves

Problem showing the saturation map of a graded ring f.g. in degree 1 induces an isomorphism of projective schemes and O(1) (The Rising Sea 15.6.G)

Equivalent definition of "regularly immersed closed subscheme" (locally Noetherian case)

Prestack of coherent sheaves

Geometry of the discriminant locus of a morphism between varieties

What means “top exterior power of the sheaf of differentials $\Omega^1_{X/Y}$” when the rank of $\Omega^1_{X/Y}$ is globally unbounded?

Noetherian induction application

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