Timeline for Finiteness of the set of $\mathbb{Q}_p$-rational periodic points
Current License: CC BY-SA 3.0
4 events
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Jan 7, 2015 at 9:50 | comment | added | naf | I don't know whether the statement holds over $\mathbb{F}_q[[T]]$. As an aside, the finiteness result (over $\mathbb{Q}_p$) can actually be extended to preperiodic points using a compactness argument, but the bound in this case actually depends on $\varphi$. | |
Jan 7, 2015 at 8:03 | comment | added | Vesselin Dimitrov | @ulrich: Thank you! Do you know if the analogous statement continues to hold over $\mathbb{F}_q[[T]]$? This appears to be left open by Fakhruddin's paper (cf. Theorem 1 (ii) and the Remark following it). | |
Jan 7, 2015 at 6:39 | comment | added | naf | This is true. See, for example, arxiv.org/abs/math/0212200. | |
Jan 7, 2015 at 0:34 | history | asked | Vesselin Dimitrov | CC BY-SA 3.0 |