An extension of Arason's theorem to certain Brauer-Severi varieties (Q1293305)

\textit{J. K. Arason} [Math. Ann. 253, 205-212 (1980; Zbl 0437.10007)] proved that the Witt ring of a projective space over a field \(k\) of characteristic not two is isomorphic to the Witt ring of \(k\). The present author establishes a similar result in the case of Severi-Brauer varieties \(X\) associated with central simple \(k-\)algebras of odd index. She shows that for such a variety the ring homomorphism \(W(k) \to W(X)\) induced by the structure morphism \(X \to \text{Spec} k\) is an isomorphism.