Timeline for On the fixed point of automorphism of $\mathbb F_3[[T]]$
Current License: CC BY-SA 3.0
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| Jun 22, 2022 at 8:13 | history | edited | CommunityBot |
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| Jul 8, 2020 at 9:00 | comment | added | R.P. | @WillSawin Well at least I sensed that something was off about the proof. Thank you Will, I appreciate this. | |
| Jul 7, 2020 at 22:09 | comment | added | Will Sawin | Since this question was just bumped, I want to point out that your too easy proof was in fact not easy enough. Say $t = a_m T^m+$ higher order terms. Then $\mathbb F_3((T))$ has dimension (at most) $m$ over $\mathbb F_3((t))$, and in fact $1, T, \dots, T^{m-1}$ form a basis, since using them and a suitable power of $t$ we can cancel the leading term of any power series, and then the next one, and the next one, and so on. | |
| Dec 17, 2013 at 22:17 | comment | added | Michael Zieve | By the way, part (1) of my answer shows that the hypotheses of the first part of your answer actually imply that $\sigma$ has order dividing $2$. | |
| Dec 17, 2013 at 22:13 | comment | added | Michael Zieve | Nice proof! So the conclusion is that $\sigma$ has a fixed point if and only if it has finite order. As I mentioned, the finite-order elements with $\sigma'(T)=1$ have been studied quite a bit; and of course, a finite-order element with $\sigma'(T)=-1$ satisfies $(\sigma^2)'(T)=1$. | |
| Dec 16, 2013 at 18:15 | comment | added | user44230 | Rene, I am satisfied and thank for Michael and Rene. Pierre | |
| Dec 16, 2013 at 17:13 | history | undeleted | R.P. | ||
| Dec 16, 2013 at 17:13 | history | edited | R.P. | CC BY-SA 3.0 |
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| Dec 16, 2013 at 17:04 | history | edited | R.P. | CC BY-SA 3.0 |
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| Dec 16, 2013 at 2:32 | history | deleted | R.P. | via Vote | |
| Dec 16, 2013 at 2:06 | history | edited | R.P. | CC BY-SA 3.0 |
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| Dec 16, 2013 at 1:28 | history | undeleted | R.P. | ||
| Dec 16, 2013 at 1:27 | history | edited | R.P. | CC BY-SA 3.0 |
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| Dec 16, 2013 at 0:47 | history | deleted | R.P. | via Vote | |
| Dec 16, 2013 at 0:41 | comment | added | Julian Rosen | Jonathan Lubin's "Torsion in the Nottingham group" discusses the structure of finite order $\sigma$. | |
| Dec 16, 2013 at 0:30 | history | answered | R.P. | CC BY-SA 3.0 |