Question

Is the construction of Zariski topology from polynomial rings functorial?

score 606 · Answer 1 · 2017-07-22 17:39:06

606

Views

Is the construction of Zariski topology from polynomial rings functorial?

Published on 22 Jul 2017 - 17:39

score 436 · Answer 2 · 2017-08-04 04:50:20

436

Views

Zariski closure of $\{(a,0) \;|\; a ∈ \Bbb Z\}$

Published on 04 Aug 2017 - 4:50

score 1.5k · Answer 3 · 2017-08-10 19:42:55

1.5k

Views

When do we say spec(R) is disconnected?

Published on 10 Aug 2017 - 19:42

score 148 · Answer 4 · 2017-09-11 17:30:54

148

Views

Regular functions which coincide in a neighbourhood

Published on 11 Sep 2017 - 17:30

score 121 · Answer 5 · 2017-10-01 19:30:59

121

Views

Given any two sets $X, Y \subset \mathbb{A}^n$, do we have $\overline{X} \times \overline {Y} = \overline {X \times Y}$?

Published on 01 Oct 2017 - 19:30

score 85 · Answer 6 · 2017-10-12 16:19:23

85

Views

Locally finite morphism implies globaly finite

Published on 12 Oct 2017 - 16:19

score 672 · Answer 7 · 2017-11-09 10:28:52

672

Views

Do irreducible sets have proper closed subsets in the Zariski topology?

Published on 09 Nov 2017 - 10:28

score 236 · Answer 8 · 2017-11-18 00:46:16

236

Views

Zariski Topology on Spec A

Published on 18 Nov 2017 - 0:46

score 416 · Answer 9 · 2017-12-05 21:13:30

416

Views

Being dense in the Zariski topology.

Published on 05 Dec 2017 - 21:13

score 236 · Answer 10 · 2017-12-06 12:43:40

on a locally noetherian scheme,can generic points of two distinct irreducible components be separated by two open sets with empty intersection?

score 890 · Answer 11 · 2017-12-06 13:44:36

890

Views

Surjectivity of the map between spectra

Published on 06 Dec 2017 - 13:44

score 307 · Answer 12 · 2017-12-22 18:12:23

307

Views

Two homogeneous polynomial of the same degree define the same projective hypersurface if and only if they are proportional

Published on 22 Dec 2017 - 18:12

score 531 · Answer 13 · 2017-12-24 13:51:21

531

Views

Is there an intrinsic or natural topology on a field, motivating the definition of the Zariski topology

Published on 24 Dec 2017 - 13:51

score 155 · Answer 14 · 2018-01-02 23:23:27

155

Views

The Zariski closure of $X$ coincides with $(\mathbb{P}^{g-1})^*$

Published on 02 Jan 2018 - 23:23

score 1.1k · Answer 15 · 2026-03-25 21:49:31

1.1k

Views

The complement of any projective hyperplane is an affine variety

Published on 25 Mar 2026 - 21:49

List Question

Is the construction of Zariski topology from polynomial rings functorial?

Zariski closure of $\{(a,0) \;|\; a ∈ \Bbb Z\}$

When do we say spec(R) is disconnected?

Regular functions which coincide in a neighbourhood

Given any two sets $X, Y \subset \mathbb{A}^n$, do we have $\overline{X} \times \overline {Y} = \overline {X \times Y}$?

Locally finite morphism implies globaly finite

Do irreducible sets have proper closed subsets in the Zariski topology?

Zariski Topology on Spec A

Being dense in the Zariski topology.

on a locally noetherian scheme,can generic points of two distinct irreducible components be separated by two open sets with empty intersection?

Surjectivity of the map between spectra

Two homogeneous polynomial of the same degree define the same projective hypersurface if and only if they are proportional

Is there an intrinsic or natural topology on a field, motivating the definition of the Zariski topology

The Zariski closure of $X$ coincides with $(\mathbb{P}^{g-1})^*$

The complement of any projective hyperplane is an affine variety

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