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Displaying similar documents to “On the µ-invariants of cyclotomic fields”

Galois module structure of ideals in wildly ramified cyclic extensions of degree p 2

Gove Griffith Elder (1995)

Annales de l'institut Fourier

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For L / K , any totally ramified cyclic extension of degree p 2 of local fields which are finite extensions of the field of p -adic numbers, we describe the ℤ p [ Gal ( L / K ) ] -module structure of each fractional ideal of L explicitly in terms of the 4 p + 1 indecomposable ℤ p [ Gal ( L / K ) ] -modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.

Some counter-examples in the theory of the Galois module structure of wild extensions

Stephen M. J. Wilson (1980)

Annales de l'institut Fourier

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Considering the ring of integers in a number field as a Z Γ -module (where Γ is a galois group of the field), one hoped to prove useful theorems about the extension of this module to a module or a lattice over a maximal order. In this paper it is show that it could be difficult to obtain, in this way, parameters which are independent of the choice of the maximal order. Several lemmas about twisted group rings are required in the proof.