Timeline for Finite extensions of $\mathbb Q_p$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Mar 3 at 11:53 | comment | added | Chris Wuthrich | The truly analogue question in char $p$ is when the coefficient field is finite. But all finite extensions of such a field are again isomorphic to a Laurent power series ring over a (possibly larger) finite field. | |
| S Mar 3 at 0:28 | history | suggested | A_S | CC BY-SA 4.0 |
some errata and tags
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| Mar 2 at 18:24 | review | Suggested edits | |||
| S Mar 3 at 0:28 | |||||
| Aug 24, 2012 at 17:57 | comment | added | Damian Rössler | See also Corollary to Prop. 4, chap. II, par. 2 of Lang "Algebraic Number Theory" (p44 second ed.). | |
| Aug 24, 2012 at 7:46 | comment | added | S. Carnahan♦ | Thank you, Jason and George. The name slipped my mind, and so did the completeness condition. | |
| Aug 23, 2012 at 12:19 | comment | added | Damian Rössler | I think you mean $k((t))$ (and not $k[[t]]$) and $k(t)$ (and not $k[t]$). | |
| Aug 23, 2012 at 11:25 | comment | added | Cyrille Corpet | @S. Carnahan: Thank you very much for this answer. Is there any way to have the same result on a purely inseparable extension of $k[[t]]$ ? | |
| Aug 23, 2012 at 11:07 | comment | added | George Lowther | The answer is no, for the reason S. Carnahan gave (think he meant complete nonarchimedean field). | |
| Aug 23, 2012 at 10:40 | comment | added | Jason Starr | I believe the result Scott is referring to is "Krasner's Lemma". | |
| Aug 23, 2012 at 10:26 | history | edited | Cyrille Corpet | CC BY-SA 3.0 |
added 7 characters in body
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| Aug 23, 2012 at 8:40 | comment | added | S. Carnahan♦ | If I'm not mistaken, the isomorphism type of a simple extension of a nonarchimedean field is locally constant with respect to the coefficients of a defining polynomial, so at least in characteristic zero, you can choose suitably nearby rational coefficients to get a number field that completes to the $p$-adic field you want. | |
| Aug 23, 2012 at 7:37 | history | asked | Cyrille Corpet | CC BY-SA 3.0 |