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Abstract.If K/F is a quadratic extension, we give necessary and sufficient conditions in terms of the discriminant (resp. the Clifford algebra) for a quadratic form of dimension 2 (resp. 4) over K to be similar to a form over F . We give similar criteria for an orthogonal involution over a central simple algebra A of degree 2 (resp. 4) over K to be such that A = A' ®F K , where A' is invariant under the involution. This leads us to an example of a quadratic form over K which is not similar to a form over F but such that the corresponding involution comes from an involution defined over F .

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