List questions from zariski-topology

Published on 07 Mar 2017 - 6:12

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Show that affine varieties are quasi-compact.

Published on 07 Mar 2017 - 20:11

148

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axiom 2 of Serre's FAC definition of algebraic variety

Published on 13 Mar 2017 - 16:52

532

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Is the axiom of choice necessary to prove that closed points in the Zariski topology are maximal ideals?

Published on 19 Mar 2017 - 17:41

75

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compactness of $\mathbb{P}_r(\mathbb{C})$ in Zariski topology

Published on 23 Mar 2017 - 22:50

63

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Geometric Picture of Open Subsets of Irreducible spaces in Zariski topology

Published on 04 Feb 2023 - 19:54

326

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Zariski topology and morphisms that coincide on a dense set

Published on 08 Feb 2023 - 13:06

148

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Showing the linear algebraic subgroup $\Bbb U_n$ of $\Bbb{GL}_n(k)$ is closed.

Published on 12 Feb 2023 - 18:17

76

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${\rm Spec}(A/\mathfrak{a})={\rm Spec}(A)$ if and only if $\mathfrak{a}$ is generated by nilpotent elements

Published on 03 Mar 2023 - 15:59

56

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Dimension of Zariski closure of an infinite discrete group

Published on 07 Mar 2023 - 20:45

101

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Let $f:A→B$ be a ring morphism and $φ : \operatorname{Spec}B→\operatorname{Spec}A$ its induced continuous map, then prove that $\rm im\ φ ⊆ V(\ker f)$

Published on 13 Mar 2023 - 17:10

229

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The Zariski topology on $\mathbb{K}^n $ is Noetherian.

Published on 15 Mar 2023 - 9:18

117

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The Lie algebra of zariski closure of an algebraic group.

Published on 15 Mar 2023 - 18:55

100

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When the Zariski topology is $T_1$ (depending on $k \ge 1)$.

Published on 16 Mar 2023 - 11:28

147

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Curves homeomorphic under Zariski topology

Published on 18 Mar 2023 - 10:36

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How to find group homomorphisms

Show that affine varieties are quasi-compact.

axiom 2 of Serre's FAC definition of algebraic variety

Is the axiom of choice necessary to prove that closed points in the Zariski topology are maximal ideals?

compactness of $\mathbb{P}_r(\mathbb{C})$ in Zariski topology

Geometric Picture of Open Subsets of Irreducible spaces in Zariski topology

Zariski topology and morphisms that coincide on a dense set

Showing the linear algebraic subgroup $\Bbb U_n$ of $\Bbb{GL}_n(k)$ is closed.

${\rm Spec}(A/\mathfrak{a})={\rm Spec}(A)$ if and only if $\mathfrak{a}$ is generated by nilpotent elements

Dimension of Zariski closure of an infinite discrete group

Let $f:A→B$ be a ring morphism and $φ : \operatorname{Spec}B→\operatorname{Spec}A$ its induced continuous map, then prove that $\rm im\ φ ⊆ V(\ker f)$

The Zariski topology on $\mathbb{K}^n $ is Noetherian.

The Lie algebra of zariski closure of an algebraic group.

When the Zariski topology is $T_1$ (depending on $k \ge 1)$.

Curves homeomorphic under Zariski topology

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