Geodesic
On the Integral Extensions of Quadratic Forms Over Local Fields
Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 297-307

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

Let F be a local field with ring of integers and unique prime ideal (p). Suppose that V a finite-dimensional regular quadratic space over F, W and W′ are two isometric subspaces of V (i.e. τ: W → W′ is an isometry from W to W′). By the well-known Witt's Theorem, τ can always be extended to an isometry σ ∈ O(V).The integral analogue of this theorem has been solved over non-dyadic local fields by James and Rosenzweig [2], over the 2-adic fields by Trojan [4], and partially over the dyadics by Hsia [1], all for the special case that W is a line. In this paper we give necessary and sufficient conditions that two arbitrary dimensional subspaces W and W′ are integrally equivalent over non-dyadic local fields. 
Band, Melvin. On the Integral Extensions of Quadratic Forms Over Local Fields. Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 297-307. doi: 10.4153/CJM-1970-037-x
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[1] 1. Hsia, J. S., Integral equivalence of vectors over depleted modular lattices on dyadic local fields, Amer. J. Math. 90 (1968), 285–294. Google Scholar

[2] 2. James, D. and Rosenzweig, S., Associated vectors in lattices over valuation rings, Amer. J. Math. 90 (1968), 295–307. Google Scholar

[3] 3. O'Meara, O. T., Introduction to quadratic forms, Die Grundlehren der mathematischen Wissenschaften, Bd. 117 (Springer-Verlag, Berlin, 1963). Google Scholar

[4] 4. Trojan, A., The integral extension of isometries of quadratic forms over local fields, Can. J. Math. 18 (1966), 920–942. Google Scholar

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