Grégory Berhuy: Réalisation de formes $\mathbb{Z}$-bilinéaires symétriques comme formes trace hermitiennes amplifiées (to appear in J. de Theorie des nombres de Bordeaux)

Submission: 2000, Apr. 10

In this paper, we show that every $\mathbb{Z}$-lattice of even rank, which is not $\mathbb{Q}$-isomorphic to the hyperbolic plane, can be realized under the form $(x,y)\in\mathfrak{A}\times\mathfrak{A}\mapsto \mathrm{Tr}_{\mathbb{Q}(\alpha)/\mathbb{Q}}(\lambda xy^\sigma)$, where $\alpha$ is an algebraic integer, $\sigma$ is a non trivial $\mathbb{Q}$-linear involution of $\mathbb{Q}(\alpha)$, $\lambda$ is a $\sigma$-symmetric element and $\mathfrak{A}$ is an ideal of $\mathbb{Z}[\alpha]$.

1991 Mathematics Subject Classification:

Keywords and Phrases:

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