The Witt group of symmetric bilinear forms over a Brauer-Severi variety with values in a line bundle (Q1818750)

Let \(X\) be the Brauer-Severi variety associated with a central simple algebra \(A\) over a field of characteristic different from two. The author computes the Witt group \(W(X,L)\) of symmetric bilinear forms over \(X\) with values in a line bundle \(L\) generating Pic\(X\). If the order of \(A\) in the Brauer group of the base field is odd, then \(W(X,L)=0\). Otherwise a set of generators for \(W(X,L)\) is exhibited.