Timeline for On exactness of the functors $M \mapsto \hat{M}$ and $M \mapsto \hat{A}\otimes_{A}M$
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Nov 9, 2013 at 4:50 | vote | accept | Alex | ||
| Nov 8, 2013 at 1:48 | answer | added | the L | timeline score: 10 | |
| Nov 8, 2013 at 0:44 | comment | added | Steven Landsburg | @KevinVentullo: You're right, of course. I overlooked this obvious counterexample. | |
| Nov 7, 2013 at 18:48 | comment | added | Jack Huizenga | You don't even have to look closely on page 109 of AM: the remark immediately follows the proposition that $\hat A$ is a flat $A$-algebra. Furthermore, the very first exercise in the section is a counterexample to exactness for non-finitely generated modules. | |
| Nov 7, 2013 at 18:23 | comment | added | Kevin Ventullo | Also, if you look closely on page 109 of A-M, there is actually a proof of the flatness of $\hat{A}$ as an $A$-algebra. | |
| Nov 7, 2013 at 18:16 | comment | added | Kevin Ventullo | In Will Sawin's setup, the injection $\mathbb{Z}\hookrightarrow \mathbb{Q}$ of $\mathbb{Z}$-modules does not remain injective after taking $p$-adic completions. | |
| Nov 7, 2013 at 18:08 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Minor language editing.
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| Nov 7, 2013 at 18:02 | history | reopened |
Steven Landsburg Benjamin Steinberg Ramiro de la Vega Kevin Walker Stefan Kohl♦ |
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| Nov 7, 2013 at 14:46 | review | Reopen votes | |||
| Nov 7, 2013 at 18:02 | |||||
| Nov 7, 2013 at 14:40 | comment | added | Steven Landsburg | Meta thread here: meta.mathoverflow.net/a/1154/10503 | |
| Nov 7, 2013 at 14:20 | comment | added | Steven Landsburg | Perhaps this question is very easy, but after a couple minutes' thought, I don't see the answer. I'm not sure why this was closed. | |
| Nov 7, 2013 at 14:18 | comment | added | Steven Landsburg | I don't understand the counterexample. A counterexample should consist of an exact sequence, not just a module. | |
| S Nov 7, 2013 at 8:52 | history | unlocked | CommunityBot | ||
| S Nov 7, 2013 at 8:52 | history | locked | CommunityBot | ||
| S Nov 7, 2013 at 8:52 | history | closed |
Jack Huizenga Kevin Ventullo Andrey Rekalo Daniel Moskovich Fernando Muro |
Not suitable for this site | |
| Nov 7, 2013 at 4:23 | comment | added | Will Sawin | For the counterexample, $A =\mathbb Z$, $I=p$, $M= \mathbb Q$. | |
| Nov 7, 2013 at 4:02 | review | Close votes | |||
| Nov 7, 2013 at 8:53 | |||||
| Nov 7, 2013 at 3:42 | review | First posts | |||
| Nov 7, 2013 at 4:43 | |||||
| Nov 7, 2013 at 3:27 | history | asked | Alex | CC BY-SA 3.0 |