Timeline for Power series $f$ such that $f(\zeta_{p^n}-1)=1/p^n$ for almost all $n \geq 0$
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Sep 10, 2010 at 19:23 | vote | accept | Tiffy | ||
| Aug 11, 2010 at 16:10 | answer | added | Laurent Berger | timeline score: 10 | |
| Aug 11, 2010 at 14:39 | comment | added | BCnrd | Can assign any values for any $n \ge 1$. Let $D$ be rigid-analytic open unit disc over $\mathbf{Q}_p$, $S$ the subset of non-rat'l pts $\zeta_ {p^n} - 1$ for $n \ge 1$. Since $S$ meets each closed disc centered at 0 in finite subset, it's "discrete" in $D$, so a 0-dimensional analytic set. Let $I$ be the radical coherent ideal of $S$ in $D$. Since $D$ is rigid-analytic Stein space (Stein exhaustion by closed discs centered at 0), ${\rm{H}}^1(D,\cdot)$ vanishes on coherent sheaves, such as $I$. So $O(D) \rightarrow (O/I)(D) = \prod_ {n \ge 1} \mathbf{Q}_ p(\zeta_ {p^n})$ is surjective. QED | |
| Aug 11, 2010 at 14:17 | history | edited | Charles Matthews | CC BY-SA 2.5 |
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| Aug 11, 2010 at 13:59 | history | asked | Tiffy | CC BY-SA 2.5 |