Timeline for Is $\widehat{\mathbb{Z}}[[t]]\cong\widehat{\mathbb{Z}}[[\widehat{\mathbb{Z}}]]$?
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11 events
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| Feb 15, 2017 at 19:05 | vote | accept | stupid_question_bot | ||
| Feb 7, 2017 at 22:01 | answer | added | Will Chen | timeline score: 7 | |
| Feb 7, 2017 at 17:26 | comment | added | stupid_question_bot | @JeremyRickard The result of Lim cited by Cor 5.9.2 seems to say that the closed multipllicative subgroup generated by $1+t$ in $\widehat{\mathbb{Z}}[[t]]$ is isomorphic to $\widehat{\mathbb{Z}}$, which certainly induces a homomorphism $\widehat{\mathbb{Z}}[[\widehat{\mathbb{Z}}]]\rightarrow\widehat{\mathbb{Z}}[[t]]$ sending "$x\mapsto 1+t$" which is an isomorphism both on the coefficient ring and on the units coming from the "group" of the completed group ring, but I suppose Ribes/Zalesski never explicitly say what the analogous statements are, so perhaps they just meant that there is an epi? | |
| Feb 7, 2017 at 17:14 | comment | added | stupid_question_bot | @JeremyRickard It seems I have both the first and the second (in the first edition it's called Cor 5.9.1b), but in both it states that the results (a),(b),(c) of 5.9.1 hold for $M(n) = \widehat{\mathbb{Z}}[[t]]$ and $F^{\text{nilp}}$ in place of $\mathbb{Z}_p[[t]]$ and $F$ the free pro-$p$ group of rank $n$. In particular, it seems that the analogue of (c) in the case $n = 1$ should be $\widehat{\mathbb{Z}}[[\widehat{\mathbb{Z}}]] = \widehat{\mathbb{Z}}[[t]]$... | |
| Feb 7, 2017 at 8:57 | comment | added | Jeremy Rickard | Which edition of Ribes-Zalesskii do you have? I have the second edition, and in that, Cor 5.9.2 is not as you state it, so maybe they've corrected it since the first edition? | |
| Feb 7, 2017 at 8:12 | answer | added | Andreas Thom | timeline score: 6 | |
| Feb 7, 2017 at 3:40 | history | edited | stupid_question_bot | CC BY-SA 3.0 |
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| Feb 7, 2017 at 3:16 | answer | added | Tom Goodwillie | timeline score: 13 | |
| Feb 6, 2017 at 22:32 | history | edited | stupid_question_bot | CC BY-SA 3.0 |
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| Feb 6, 2017 at 19:47 | history | edited | stupid_question_bot | CC BY-SA 3.0 |
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| Feb 6, 2017 at 8:21 | history | asked | stupid_question_bot | CC BY-SA 3.0 |