Timeline for $p$-adic completeness of the ring of Witt vectors
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jun 8, 2016 at 8:00 | history | bounty ended | Lisa S. | ||
| S Jun 8, 2016 at 8:00 | history | notice removed | Lisa S. | ||
| Jun 7, 2016 at 19:22 | vote | accept | Lisa S. | ||
| Jun 7, 2016 at 15:44 | answer | added | Oli Gregory | timeline score: 2 | |
| Jun 7, 2016 at 15:08 | comment | added | Lisa S. | @OliGregory: Thanks! You should post this as an answer: as far as I can tell the reference you give resolves the question. | |
| Jun 7, 2016 at 8:29 | comment | added | Oli Gregory | Perhaps you already know this, but page 11, proposition 3 (and the subsequent sub-lemmas) of Zink's "The display of a formal $p$-divisible group" looks relevant. Here's the address of the paper on his website... math.uni-bielefeld.de/~zink/display.pdf | |
| S Jun 7, 2016 at 6:23 | history | bounty started | Lisa S. | ||
| S Jun 7, 2016 at 6:23 | history | notice added | Lisa S. | Draw attention | |
| Jun 4, 2016 at 13:17 | comment | added | YCor | @znt if $G$ is a compact abelian group such that for all $x$, $p^nx\to 0$ when $n\to\infty$ and $G$ torsion-free, then $G$ is isomorphic to some power of $\mathbf{Z}_p$. This is easy to establish with Pontryagin duality (because the Pontryagin dual is a discrete, divisible abelian group in which every element is killed by some power of $p$, hence is a direct sum of copies of $\mathbf{Z}[1/p]/\mathbf{Z}$). | |
| Jun 4, 2016 at 12:18 | comment | added | znt | I believe that the p-Witt vectors for $\mathbf{Z}_p$ is isomorphic, as an abelian group, to a product of countably infinitely many copies of $\mathbf{Z}_p$ (I believe this because if memory serves then Hendrik Lenstra told me this in 2002, and if it's wrong then it's my memory at fault), and the p-Witt vectors for $\mathbf{Z}/p^m$ is isomorphic as an abelian group to a product of $\mathbf{Z}_p$ and countably infinitely many copies of $\mathbf{Z}/p^{m-1}$ (with the same reference and caveat). So there are least are some examples when it's true. | |
| Jun 4, 2016 at 10:46 | history | asked | Lisa S. | CC BY-SA 3.0 |