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Biquadratic extensions with one break. (English) Zbl 1033.11054

Let \(K\) be a finite extension of the field of \(2\)-adic numbers, and consider totally ramified biquadratic extensions \(N/K\) with Galois group \(G\). The ramification filtration of \(G\) (with lower numbering) contains one or two breaks; the Galois module structure of ideals in extensions with two breaks were studied by the second author [Can. J. Math. 50, 1007–1047 (1998; Zbl 1015.11056)]. In this article, the authors treat the more complicated case of fields with one break and show explicitly how the ideals \({\mathfrak P}^i\) in \(N\) decompose into indecomposable \({\mathbb Z}_2[G]\)-modules.

MSC:

11S15 Ramification and extension theory
11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers
20C11 \(p\)-adic representations of finite groups

Citations:

Zbl 1015.11056
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