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Galois module structure of the integers in wildly ramified $C_p\times C_p$ extensions

  Published:1997-08-01
 Printed: Aug 1997
  • G. Griffith Elder
  • Manohar L. Madan
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Abstract

Let $L/K$ be a finite Galois extension of local fields which are finite extensions of $\bQ_p$, the field of $p$-adic numbers. Let $\Gal (L/K)=G$, and $\euO_L$ and $\bZ_p$ be the rings of integers in $L$ and $\bQ_p$, respectively. And let $\euP_L$ denote the maximal ideal of $\euO_L$. We determine, explicitly in terms of specific indecomposable $\bZ_p[G]$-modules, the $\bZ_p[G]$-module structure of $\euO_L$ and $\euP_L$, for $L$, a composite of two arithmetically disjoint, ramified cyclic extensions of $K$, one of which is only weakly ramified in the sense of Erez \cite{erez}.
Keywords: Galois module structure---integral representation. Galois module structure---integral representation.
MSC Classifications: 11S15, 20C32 show english descriptions Ramification and extension theory
Representations of infinite symmetric groups
11S15 - Ramification and extension theory
20C32 - Representations of infinite symmetric groups
 

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