Question

Are open subschemes "nicer" than closed subschmes?

score 42 · Answer 1 · 2026-04-11 12:53:53

42

Views

Are open subschemes "nicer" than closed subschmes?

Published on 11 Apr 2026 - 12:53

score 261 · Answer 2 · 2021-08-10 14:28:53

261

Views

If $X$ is reduced scheme then same morphism on k-rational points is the same.

Published on 10 Aug 2021 - 14:28

score 129 · Answer 3 · 2026-04-13 04:49:00

129

Views

Spacetime as an algebraic surface over $\mathbb{C}$

Published on 13 Apr 2026 - 4:49

score 137 · Answer 4 · 2026-04-09 10:04:17

137

Views

$\mathbb Z$ as an example of scheme

Published on 09 Apr 2026 - 10:04

score 102 · Answer 5 · 2026-03-28 15:21:17

102

Views

Confusion about a standard rational map $\operatorname{Proj} A[x_0,\dots,x_n] \dashrightarrow \operatorname{Proj} A[x_0,\dots,x_{n-1}]$.

Published on 28 Mar 2026 - 15:21

score 174 · Answer 6 · 2026-04-12 11:46:22

174

Views

Example of a non-affine scheme whose reduction is affine

Published on 12 Apr 2026 - 11:46

score 57 · Answer 7 · 2026-04-12 08:02:24

Is it true that if $\pi: X \dashrightarrow Y$ is a dominant rational map, then for every representative $U \to Y$, the image is dense in $Y$?

score 154 · Answer 8 · 2026-03-28 04:35:12

154

Views

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

Published on 28 Mar 2026 - 4:35

score 85 · Answer 9 · 2026-04-12 18:43:20

85

Views

If $X$ and $Y$ are birational then there is a dense open subscheme $U$ of $X$ and a dense open subscheme $V$ of $Y$ such that $U \cong V$.

Published on 12 Apr 2026 - 18:43

score 158 · Answer 10 · 2026-04-12 21:39:06

158

Views

Let $f: X \to Y$ be a finite morphism of nonsingular curves. Then $f^*: \operatorname{Div} Y \to \operatorname{Div} X$ preserves linear equivalence.

Published on 12 Apr 2026 - 21:39

score 586 · Answer 11 · 2026-04-12 08:17:09

586

Views

Criterion for a group scheme to be smooth

Published on 12 Apr 2026 - 8:17

score 618 · Answer 12 · 2026-04-11 18:41:05

618

Views

Torsion subsheaf of coherent sheaf on locally Noetherian scheme

Published on 11 Apr 2026 - 18:41

score 262 · Answer 13 · 2026-04-12 02:13:05

262

Views

Graded Ring and Projective Spaces.

Published on 12 Apr 2026 - 2:13

score 223 · Answer 14 · 2026-04-11 21:25:39

223

Views

If $i: U \to Z$ is an open embedding of schemes, and $\rho: Y \to Z$ is any morphism of schemes, how do we know $U \times_Z Y = \rho^{-1}(U)$?

Published on 11 Apr 2026 - 21:25

score 255 · Answer 15 · 2026-04-09 04:37:14

255

Views

Does pushforward commute with tensor for coherent sheaves under an open immersion?

Published on 09 Apr 2026 - 4:37

List Question

Are open subschemes "nicer" than closed subschmes?

If $X$ is reduced scheme then same morphism on k-rational points is the same.

Spacetime as an algebraic surface over $\mathbb{C}$

$\mathbb Z$ as an example of scheme

Confusion about a standard rational map $\operatorname{Proj} A[x_0,\dots,x_n] \dashrightarrow \operatorname{Proj} A[x_0,\dots,x_{n-1}]$.

Example of a non-affine scheme whose reduction is affine

Is it true that if $\pi: X \dashrightarrow Y$ is a dominant rational map, then for every representative $U \to Y$, the image is dense in $Y$?

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

If $X$ and $Y$ are birational then there is a dense open subscheme $U$ of $X$ and a dense open subscheme $V$ of $Y$ such that $U \cong V$.

Let $f: X \to Y$ be a finite morphism of nonsingular curves. Then $f^*: \operatorname{Div} Y \to \operatorname{Div} X$ preserves linear equivalence.

Criterion for a group scheme to be smooth

Torsion subsheaf of coherent sheaf on locally Noetherian scheme

Graded Ring and Projective Spaces.

If $i: U \to Z$ is an open embedding of schemes, and $\rho: Y \to Z$ is any morphism of schemes, how do we know $U \times_Z Y = \rho^{-1}(U)$?

Does pushforward commute with tensor for coherent sheaves under an open immersion?

Trending Questions

Popular # Hahtags

Popular Questions