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Galois Module Structure of the Integers in Wildly Ramified Cp × Cp Extensions

  • G. Griffith Elder (a1) and Manohar L. Madan (a2)

Abstract

Let L/K be a finite Galois extension of local fields which are finite extensions of ℚ p , the field of p-adic numbers. Let Gal(L/K) = G, and 𝔒 L and ℤ p be the rings of integers in L and ℚ p , respectively. And let 𝔓 L denote the maximal ideal of 𝔒 L . We determine, explicitly in terms of specific indecomposable ℤ p [G]-modules, the ℤ p [G]-module structure of 𝔒 L and 𝔓 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 [6].

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References

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Galois Module Structure of the Integers in Wildly Ramified Cp × Cp Extensions

  • G. Griffith Elder (a1) and Manohar L. Madan (a2)

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