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.

Let k be a finite extension of 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 KΓ unless k= p . We determine explicitly under the hypothesis that the absolute ramification index of k is sufficiently large.

Soit k une extension finie de 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 p l’anneau de valuation de k 3 n’est pas libre sur son ordre associé 𝔄 dans KΓ. Nous explicitons 𝔄 dans le cas où l’indice absolu de ramification de k est assez grand.

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},
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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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