Associated orders of certain extensions arising from Lubin-Tate formal groups

Nigel P. Byott

doi:10.5802/jtnb.212

Nigel P. Byott

Journal de Théorie des Nombres de Bordeaux, Volume 9 (1997) no. 2, pp. 449-462.

Abstract
Résumé

Let $k$ be a finite extension of $ℚ_{p}$ , let $k_{1}$ , respectively $k_{3}$ , be the division fields of level $1$ , respectively $3$ , arising from a Lubin-Tate formal group over $k$ , and let $Γ =$ Gal( $k_{3} / k_{1}$ ). It is known that the valuation ring $k_{3}$ cannot be free over its associated order $𝔄$ in $K Γ$ unless $k = ℚ_{p}$ . We determine explicitly under the hypothesis that the absolute ramification index of $k$ is sufficiently large.

Soit $k$ une extension finie de $ℚ_{p}, k_{1}$ et $k_{3}$ les corps de division de niveaux respectifs $1$ et $3$ associés à un groupe formel de Lubin-Tate, et soit $Γ =$ Gal( $k_{3} / k_{1}$ ). On sait que si $k \neq ℚ_{p}$ l’anneau de valuation de $k_{3}$ n’est pas libre sur son ordre associé $𝔄$ dans $K Γ$ . Nous explicitons $𝔄$ dans le cas où l’indice absolu de ramification de $k$ est assez grand.

MR: 1617408 | Zbl: 0902.11052

DOI: 10.5802/jtnb.212
Classification: 11S23, 11S31, 11R33
Keywords: associated order, Lubin-Tate formal group

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     title = {Associated orders of certain extensions arising from {Lubin-Tate} formal groups},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {449--462},
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Nigel P. Byott. Associated orders of certain extensions arising from Lubin-Tate formal groups. Journal de Théorie des Nombres de Bordeaux, Volume 9 (1997) no. 2, pp. 449-462. doi : 10.5802/jtnb.212. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.212/

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