Let be a finite extension of , let , respectively , be the division fields of level , respectively , arising from a Lubin-Tate formal group over , and let Gal(). It is known that the valuation ring cannot be free over its associated order in unless . We determine explicitly under the hypothesis that the absolute ramification index of is sufficiently large.
Soit une extension finie de et les corps de division de niveaux respectifs et associés à un groupe formel de Lubin-Tate, et soit Gal(). On sait que si l’anneau de valuation de n’est pas libre sur son ordre associé dans . Nous explicitons dans le cas où l’indice absolu de ramification de est assez grand.
Classification: 11S23, 11S31, 11R33
Keywords: associated order, Lubin-Tate formal group
@article{JTNB_1997__9_2_449_0, 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}, doi = {10.5802/jtnb.212}, zbl = {0902.11052}, mrnumber = {1617408}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.212/} }
TY - JOUR TI - Associated orders of certain extensions arising from Lubin-Tate formal groups JO - Journal de Théorie des Nombres de Bordeaux PY - 1997 DA - 1997/// SP - 449 EP - 462 VL - 9 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.212/ UR - https://zbmath.org/?q=an%3A0902.11052 UR - https://www.ams.org/mathscinet-getitem?mr=1617408 UR - https://doi.org/10.5802/jtnb.212 DO - 10.5802/jtnb.212 LA - en ID - JTNB_1997__9_2_449_0 ER -
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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