Question

Commutative algebra: Irreducible components of $\operatorname{Spec}(A)$

score 92 · Answer 1 · 2023-03-18 14:34:03

92

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Commutative algebra: Irreducible components of $\operatorname{Spec}(A)$

Published on 18 Mar 2023 - 14:34

score 37 · Answer 2 · 2023-03-22 16:15:49

37

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Is "Zariski connected" equivalent to "ring connected"?

Published on 22 Mar 2023 - 16:15

score 71 · Answer 3 · 2023-04-18 08:20:34

71

Views

If the product of closed sets is closed in the product topology shouldn't {(0,0)} be closed in $A^1 \times A^1$ zariski topology.

Published on 18 Apr 2023 - 8:20

score 173 · Answer 4 · 2023-04-22 16:43:17

173

Views

Can $\operatorname{Spec}(R)$ be not homeomorphic to $\operatorname{Spec}(S)$ but be isomorphic as a poset?

Published on 22 Apr 2023 - 16:43

score 56 · Answer 5 · 2023-05-07 11:22:11

56

Views

$X\times Y$ and the product topology

Published on 07 May 2023 - 11:22

score 71 · Answer 6 · 2023-05-19 12:53:31

71

Views

Let $G$ be a linear algebraic group and $C_G(x)$ be the centralizer of $x$. Show that $C_G(x)$ is a closed subgroup for all $x\in G$.

Published on 19 May 2023 - 12:53

score 82 · Answer 7 · 2023-05-29 10:42:45

82

Views

How exactly does Zariski-Topology relate to Standard topology on $\Bbb{C}$?

Published on 29 May 2023 - 10:42

score 244 · Answer 8 · 2023-06-01 23:55:01

244

Views

Salvaging Exercise 3.2.10(2) of Springer's, "Linear Algebraic Groups (Second Edition)".

Published on 01 Jun 2023 - 23:55

score 56 · Answer 9 · 2023-06-02 11:35:40

56

Views

Why is the graph of polynomial closed in Zariski-Topology?

Published on 02 Jun 2023 - 11:35

score 114 · Answer 10 · 2026-03-25 20:42:00

114

Views

Compute the Zariski closure of a set

Published on 25 Mar 2026 - 20:42

score 121 · Answer 11 · 2023-06-27 21:35:20

121

Views

The torsion subgroup of a diagonalisable linear algebraic group $G$ with ${\rm char}(k)=p$ (alg. closed $k$) is dense in $G$

Published on 27 Jun 2023 - 21:35

score 48 · Answer 12 · 2023-06-30 20:41:46

Computing the Annihilator and Zariski closure of $Z = \lbrace (t, t^2, t^3) \mid t \in \mathbb{C} \rbrace \subseteq \mathbb{A}^3(\mathbb{C})$

score 86 · Answer 13 · 2023-07-04 22:34:13

86

Views

Let $\mathfrak{A}$ be a finite dimensional $k$-algebra for alg. closed $k$. Prove ${\rm Aut}(\mathfrak{A})$ is a closed subgroup of $GL(\mathfrak{A})$

Published on 04 Jul 2023 - 22:34

score 54 · Answer 14 · 2023-07-08 19:08:59

54

Views

Is a closed, nonempty subset of a (linear) algebraic group $G$ that is closed under taking products a subgroup of $G$?

Published on 08 Jul 2023 - 19:08

score 17 · Answer 15 · 2026-03-14 01:56:43

17

Views

How to calculate the Zariski closure of $Z(A)B$?

Published on 14 Mar 2026 - 1:56

List Question

Commutative algebra: Irreducible components of $\operatorname{Spec}(A)$

Is "Zariski connected" equivalent to "ring connected"?

If the product of closed sets is closed in the product topology shouldn't {(0,0)} be closed in $A^1 \times A^1$ zariski topology.

Can $\operatorname{Spec}(R)$ be not homeomorphic to $\operatorname{Spec}(S)$ but be isomorphic as a poset?

$X\times Y$ and the product topology

Let $G$ be a linear algebraic group and $C_G(x)$ be the centralizer of $x$. Show that $C_G(x)$ is a closed subgroup for all $x\in G$.

How exactly does Zariski-Topology relate to Standard topology on $\Bbb{C}$?

Salvaging Exercise 3.2.10(2) of Springer's, "Linear Algebraic Groups (Second Edition)".

Why is the graph of polynomial closed in Zariski-Topology?

Compute the Zariski closure of a set

The torsion subgroup of a diagonalisable linear algebraic group $G$ with ${\rm char}(k)=p$ (alg. closed $k$) is dense in $G$

Computing the Annihilator and Zariski closure of $Z = \lbrace (t, t^2, t^3) \mid t \in \mathbb{C} \rbrace \subseteq \mathbb{A}^3(\mathbb{C})$

Let $\mathfrak{A}$ be a finite dimensional $k$-algebra for alg. closed $k$. Prove ${\rm Aut}(\mathfrak{A})$ is a closed subgroup of $GL(\mathfrak{A})$

Is a closed, nonempty subset of a (linear) algebraic group $G$ that is closed under taking products a subgroup of $G$?

How to calculate the Zariski closure of $Z(A)B$?

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