Timeline for Uniformizer for splitting field of p^{1/p^n} over p-adics
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 4, 2019 at 19:15 | comment | added | David Lampert | Maybe my p=3 calculations are wrong (I did them years ago and without computer). Anyway the method (for any p) and the p=2 result are correct. | |
| Nov 4, 2019 at 5:53 | comment | added | Yijun Yuan | Well, I calculated the case of p=3 yesterday, but it seems to me that the element(let's call it $\pi$) you give has valuation 6. With the help of Mathematica, its minimal polynomial is $729+\cdots+627342091483343791624192x^{54}$, where this large constant is coprime to 3. Thus, $v(\pi)=v(729/627...192)/54=v(729)/54=6v(3)=v(3)/9=6$. Tell me if I'm wrong. | |
| Nov 3, 2019 at 21:39 | comment | added | David Lampert | Algebraic P-adic Expansions explains how to calculate p-adic expansions with some results about roots of unity (I think the statements there about $p^2$-roots of unity maybe technically incorrect and the "Edit: With p=3" is correct). The element identified is a uniformizer because its valuation is 1/(ramification index). | |
| Nov 3, 2019 at 11:23 | comment | added | Yijun Yuan | Could you please explain more? 1. How do you calculate the p-adic expansion of the unit root? 2. Why the element you find is a uniformizer? | |
| Mar 10, 2016 at 22:51 | history | edited | David Lampert | CC BY-SA 3.0 |
added 218 characters in body
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| Feb 9, 2016 at 14:59 | history | answered | David Lampert | CC BY-SA 3.0 |