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Galois Module Structure of the Integers in Wildly Ramified Cp × Cp Extensions
Published online by Cambridge University Press: 20 November 2018
Abstract
Let L/K be a finite Galois extension of local fields which are finite extensions of ℚp, the field of p-adic numbers. Let Gal(L/K) = G, and 𝔒L and ℤp be the rings of integers in L and ℚp, respectively. And let 𝔓L denote the maximal ideal of 𝔒L. We determine, explicitly in terms of specific indecomposable ℤp[G]-modules, the ℤp[G]-module structure of 𝔒L and 𝔓L, 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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- Copyright © Canadian Mathematical Society 1997
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