Timeline for Is the positive part of an algebraic bilateral p-adic convergent power series algebraic?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 8, 2016 at 10:41 | comment | added | Mark Wildon | That was my guess, and it still looks plausible to me now. But I don't have a proof. | |
| Apr 8, 2016 at 7:05 | comment | added | js21 | Should I understand that if $f = (1-p(X+X^{-1})^{-1}$, then $f_+$ is not in $\mathbb{Z}_p\{X\}$ ? | |
| Apr 8, 2016 at 6:57 | comment | added | js21 | You can look into Raynaud's "Anneaux henseliens". If $B$ is the integral closure of $\mathbb{Z}_p[X]$ in $\mathbb{Z}_p \langle X \rangle$, then $\mathbb{Z}_p \{ X\}$ is the localization of $B$ w.r.t $1 + B \cap p\mathbb{Z}_p \langle X \rangle$. The same construction applies to $\mathbb{Z}_p [X,X^{-1} ]$. In particular $(1-p(X+X^{-1})^{-1}$ is in $\mathbb{Z}_p\{X,X^{-1}\}$. | |
| Apr 6, 2016 at 19:23 | comment | added | Mark Wildon | Please could you give a reference for the definitions of $\mathbb{Z}_p\{X\}$ and $\mathbb{Z}_p\{X,X^{-1}\}$, or include them in the question? (I am not an expert, so am guessing slightly what Henselization means in this context.) Specifically, is is true that $(1-p(X+X^{-1})^{-1}$ is in $\mathbb{Z}_p\{X,X^{-1}\}$? | |
| Apr 4, 2016 at 9:57 | history | asked | js21 | CC BY-SA 3.0 |