Geodesic
The Integral Extension of Isometries of Quadratic Forms Over Local Fields
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 920-942

Voir la notice de l'article provenant de la source Cambridge University Press

Let F be a local field with ring of integers 0 and prime ideal π0. If V is a vector space over F, a lattice L in F is defined as an 0-module in the vector space V with the property that the elements of L have bounded denominators in the basis for V. If V is, in addition, a quadratic space, the lattice L then has a quadratic structure superimposed on it. Two lattices on V are then said to be isometric if there is an isometry of V that maps one onto the other.In this paper, we consider the following problem: given two elements, v and w, of the lattice L over the regular quadratic space V, find necessary and sufficient conditions for the existence of an isometry on L that maps v onto w. 
Trojan, Allan. The Integral Extension of Isometries of Quadratic Forms Over Local Fields. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 920-942. doi: 10.4153/CJM-1966-092-x
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