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

Journal de théorie des nombres de Bordeaux (1997)

- Volume: 9, Issue: 2, page 449-462
- ISSN: 1246-7405

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topByott, Nigel P.. "Associated orders of certain extensions arising from Lubin-Tate formal groups." Journal de théorie des nombres de Bordeaux 9.2 (1997): 449-462. <http://eudml.org/doc/247989>.

@article{Byott1997,

abstract = {Let $k$ be a finite extension of $\mathbb \{Q\}_p$, 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 $\Gamma =$ Gal($k_3/k_1$). It is known that the valuation ring $k_3$ cannot be free over its associated order $\mathfrak \{A\}$ in $K \Gamma $ unless $k = \mathbb \{Q\}_p$. We determine explicitly under the hypothesis that the absolute ramification index of $k$ is sufficiently large.},

author = {Byott, Nigel P.},

journal = {Journal de théorie des nombres de Bordeaux},

keywords = {associated order; Lubin-Tate formal group; associated orders; Galois modules; ramification; Lubin-Tate extensions; divisibility properties of binomial coefficients},

language = {eng},

number = {2},

pages = {449-462},

publisher = {Université Bordeaux I},

title = {Associated orders of certain extensions arising from Lubin-Tate formal groups},

url = {http://eudml.org/doc/247989},

volume = {9},

year = {1997},

}

TY - JOUR

AU - Byott, Nigel P.

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

JO - Journal de théorie des nombres de Bordeaux

PY - 1997

PB - Université Bordeaux I

VL - 9

IS - 2

SP - 449

EP - 462

AB - Let $k$ be a finite extension of $\mathbb {Q}_p$, 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 $\Gamma =$ Gal($k_3/k_1$). It is known that the valuation ring $k_3$ cannot be free over its associated order $\mathfrak {A}$ in $K \Gamma $ unless $k = \mathbb {Q}_p$. We determine explicitly under the hypothesis that the absolute ramification index of $k$ is sufficiently large.

LA - eng

KW - associated order; Lubin-Tate formal group; associated orders; Galois modules; ramification; Lubin-Tate extensions; divisibility properties of binomial coefficients

UR - http://eudml.org/doc/247989

ER -

## References

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- [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 Bordeaux9 (1997), 201-219. Zbl0889.11040MR1469668
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- [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. Zbl0816.11061MR1299647
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- [S] J.-P. Serre, Local Class Field Theory, in Algebraic Number Theory (J.W.S. Cassels and A. Fröhlich, eds.), Academic Press, 1967. MR220701
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