Question

Vakil's Exercise 1.3.L.: Tensor products and localization of modules

score 145 · Answer 1 · 2019-09-19 23:16:07

145

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Vakil's Exercise 1.3.L.: Tensor products and localization of modules

Published on 19 Sep 2019 - 23:16

score 116 · Answer 2 · 2019-09-20 13:03:23

116

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Find $\operatorname{Supp}_\mathbb Z(\mathbb Q/\mathbb Z)$ and $\operatorname{Ass}_\mathbb Z(\mathbb Q/\mathbb Z)$.

Published on 20 Sep 2019 - 13:03

score 120 · Answer 3 · 2019-09-20 19:33:53

120

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If $I$ is an ideal and $M$ is a (finitely generated) module then $\text{Supp}(M/IM)\subseteq_{(=)}\text{Supp}(M)\cap V(I)$

Published on 20 Sep 2019 - 19:33

score 132 · Answer 4 · 2019-09-21 17:02:54

132

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If $M_p$ is a localization, why doesn't $M_p=0$ imply $M=0$?

Published on 21 Sep 2019 - 17:02

score 188 · Answer 5 · 2019-09-23 20:35:33

188

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Calculus of fractions and Serre subcategories

Published on 23 Sep 2019 - 20:35

score 78 · Answer 6 · 2019-09-25 21:08:25

78

Views

Is $U^{-1} (A \otimes_R A) \cong U^{-1} A \otimes_R U^{-1} A$?

Published on 25 Sep 2019 - 21:08

score 112 · Answer 7 · 2026-03-25 12:50:57

112

Views

If $R$ is not a local ring can we say that $R_p$ is not faithfully flat as an $R$- module for any prime ideal $p$ of $R$?

Published on 25 Mar 2026 - 12:50

score 592 · Answer 8 · 2019-09-27 08:54:42

592

Views

$R_f \cong R[x]/(fx-1)$

Published on 27 Sep 2019 - 8:54

score 128 · Answer 9 · 2026-03-25 19:25:04

128

Views

Show that this functor is a localization

Published on 25 Mar 2026 - 19:25

score 557 · Answer 10 · 2014-03-13 14:52:51

557

Views

If $M$ is a maximal ideal of a commutative ring R, then $R/M \cong R_M/M_M$.

Published on 13 Mar 2014 - 14:52

score 743 · Answer 11 · 2014-06-26 06:39:47

743

Views

Can zero divisors be in the denominator when we localize rings?

Published on 26 Jun 2014 - 6:39

score 109 · Answer 12 · 2014-09-21 07:30:49

109

Views

A question regarding the definition of localization of ring

Published on 21 Sep 2014 - 7:30

score 185 · Answer 13 · 2026-03-25 01:16:33

185

Views

$S$-local objects of presheaves are reflective and characterize local presentability

Published on 25 Mar 2026 - 1:16

score 417 · Answer 14 · 2026-03-26 19:35:46

417

Views

Finitely generated submodule of a localisation

Published on 26 Mar 2026 - 19:35

score 603 · Answer 15 · 2014-11-17 04:18:15

603

Views

Interpretation of hint for Exercise 2.19b of Eisenbud

Published on 17 Nov 2014 - 4:18

List Question

Vakil's Exercise 1.3.L.: Tensor products and localization of modules

Find $\operatorname{Supp}_\mathbb Z(\mathbb Q/\mathbb Z)$ and $\operatorname{Ass}_\mathbb Z(\mathbb Q/\mathbb Z)$.

If $I$ is an ideal and $M$ is a (finitely generated) module then $\text{Supp}(M/IM)\subseteq_{(=)}\text{Supp}(M)\cap V(I)$

If $M_p$ is a localization, why doesn't $M_p=0$ imply $M=0$?

Calculus of fractions and Serre subcategories

Is $U^{-1} (A \otimes_R A) \cong U^{-1} A \otimes_R U^{-1} A$?

If $R$ is not a local ring can we say that $R_p$ is not faithfully flat as an $R$- module for any prime ideal $p$ of $R$?

$R_f \cong R[x]/(fx-1)$

Show that this functor is a localization

If $M$ is a maximal ideal of a commutative ring R, then $R/M \cong R_M/M_M$.

Can zero divisors be in the denominator when we localize rings?

A question regarding the definition of localization of ring

$S$-local objects of presheaves are reflective and characterize local presentability

Finitely generated submodule of a localisation

Interpretation of hint for Exercise 2.19b of Eisenbud

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