Timeline for A confusion about power series and p-adic measures
Current License: CC BY-SA 4.0
10 events
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| Oct 16, 2022 at 19:22 | history | edited | KConrad | CC BY-SA 4.0 |
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| May 12, 2022 at 20:21 | comment | added | KConrad | My comments about degree-by-degree arguments now reminds me of Lubin's description of the development of Lubin-Tate theory on the MO page mathoverflow.net/questions/220796/motivating-lubin-tate-theory, where he writes "I used extremely tiresome degree-by-degree methods based on the techniques of Lazard" until he made a discovery that led Tate to the important Lemma 1 of their 1965 Annals paper, which codifies many degree-by-degree arguments into a single setting so you don't have to go through that actual process directly all the time. | |
| May 12, 2022 at 20:13 | comment | added | KConrad | It's a good exercise to go through that Niven paper on formal power series and prove the results using Hensel's lemma and the $x$-adic topology in place of degree-by-degree arguments, in his $\mathbf C[[x]]$ (which he writes as $P$) or in $A[[x]]$ when possible (sometimes $A$ has to be a field of characteristic $0$). For example, Theorem 1 in $A[[x]]$ is saying $A[[x]]^\times$ is the series with constant term in $A^\times$ (use Hensel's lemma) and Theorem 3 is saying each $\alpha \in 1 + xA[[x]]$ has a unique $n$th root in $1+xA[[x]]$ if $n \in A^\times$ (Hensel's lemma on $y^n - \alpha$). | |
| May 12, 2022 at 19:31 | comment | added | Adithya Chakravarthy | thanks a ton! this second way of thinking about power series composition is very illuminating. I appreciate the help :) | |
| May 12, 2022 at 19:31 | vote | accept | Adithya Chakravarthy | ||
| May 12, 2022 at 17:42 | history | edited | KConrad | CC BY-SA 4.0 |
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| May 12, 2022 at 17:34 | history | edited | KConrad | CC BY-SA 4.0 |
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| May 12, 2022 at 16:29 | history | edited | KConrad | CC BY-SA 4.0 |
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| May 12, 2022 at 16:19 | history | edited | KConrad | CC BY-SA 4.0 |
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| May 12, 2022 at 16:12 | history | answered | KConrad | CC BY-SA 4.0 |