## On the Hermitian structure of the square root of the inverse different. (Sur la structure hermitienne de la racine carrée de la codifférente.)(French)Zbl 0789.11062

Let $$K$$ be a number field which is Galois over $$\mathbb{Q}$$, of odd degree and let $$G$$ be its Galois group. There is a unique fractional ideal of $$K$$ which is unimodular for the quadratic form $$\text{Trace}_{K/ \mathbb{Q}} (x^ 2)$$. This ideal is the square root of the inverse different, and is denoted $$A_ K$$. In this paper, we describe an explicit representative of the $$\mathbb{Z}[G]$$-isometry class of $$(A_ K,\text{Trace}_{K/ \mathbb{Q}}(x^ 2))$$, which depends only on the wildly ramified prime numbers $$p$$ having a ramification index in $$K$$ different from $$p$$.

### MSC:

 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers 11E39 Bilinear and Hermitian forms
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### References:

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