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.

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.

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.

Classification : 11S23, 11S31, 11R33
Mots clés : 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},
     publisher = {Universit\'e Bordeaux I},
     volume = {9},
     number = {2},
     year = {1997},
     zbl = {0902.11052},
     mrnumber = {1617408},
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     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/

[B1] N.P. Byott, Some self-dual rings of integers not free over their associated orders, Math. Proc. Camb. Phil. Soc. 110 (1991), 5-10; Corrigendum, 116 (1994), 569. | MR

[B2] N.P. Byott, Galois structure of ideals in wildly ramified abelian p-extensions of a p-adic field, and some applications, J. de Théorie des Nombres de Bordeaux 9 (1997), 201-219. | Numdam | MR | Zbl

[C] S.-P. Chan, Galois module structure of non-Kummer extensions, Preprint, National University of Singapore (1995). | MR

[C-L] S.-P. Chan and C.-H. Lim, The associated orders of rings of integers in Lubin- Tate division fields over the p-adic number field, Ill. J. Math. 39 (1995), 30-38. | MR | Zbl

[R] P. Ribenboim, The Book of Prime Number Records, 2nd edition, Springer, 1989. | MR | Zbl

[S] J.-P. Serre, Local Class Field Theory, in Algebraic Number Theory (J.W.S. Cassels and A. Fröhlich, eds.), Academic Press, 1967. | MR

[T] M.J. Taylor, Formal groups and the Galois module structure of local rings of integers, J. reine angew. Math. 358 (1985), 97-103. | MR | Zbl