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

Nigel P. Byott

Nigel P. Byott

Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 2, pp. 449-462.

Résumé
Abstract

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.

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.

MR Zbl

Classification : 11S23, 11S31, 11R33
Mots clés : associated order, Lubin-Tate formal group

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     author = {Nigel P. Byott},
     title = {Associated orders of certain extensions arising from {Lubin-Tate} formal groups},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {449--462},
     publisher = {Universit\'e Bordeaux I},
     volume = {9},
     number = {2},
     year = {1997},
     zbl = {0902.11052},
     mrnumber = {1617408},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1997__9_2_449_0/}
}

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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, Tome 9 (1997) no. 2, pp. 449-462. https://jtnb.centre-mersenne.org/item/JTNB_1997__9_2_449_0/

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