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A countrexample in the Galois module structure of wild extensions of the rational field

Stephen M. J. Wilson

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Galois module structure of the rings of integers in wildly ramified extensions

Stephen M. J. Wilson — 1989

Annales de l'institut Fourier

The main results of this paper may be loosely stated as follows. Theorem.— Let $N$ and $N^{'}$ be sums of Galois algebras with group $Γ$ over algebraic number fields. Suppose that $N$ and $N^{'}$ have the same dimension $ℚ$ and that they are identical at their wildly ramified primes. Then (writing $𝒪_{N}$ for the maximal order in $N$ ) $𝒪_{N} \oplus 𝒪_{N} \oplus ℤ Γ ≅_{ℤ Γ} \oplus 𝒪_{N}^{'} \oplus 𝒪_{N^{'}} \oplus ℤ Γ .$ In...

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

Stephen M. J. Wilson — 1980

Annales de l'institut Fourier

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.

Alexander ideals of classical knots.

Cherry Kearton; Stephen M. J. Wilson — 1997

Publicacions Matemàtiques

The Alexander ideals of classical knots are characterised, a result which extends to certain higher dimensional knots.

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