RÉSUMÉ

For an orthogonal Galois representation, its second Stiefel-Whitney class is an element in the 2-torsion of the Brauer group. It is related to the local constant of the functional equation of the L-function. For a representation associated to a finite separable extension, Serre proved that it is related with the quadratic form Tr(x^2). We consider a generalization of this relation to higher dimension.

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