A note on splitting quadratic forms
Let \(F\) be a global function field of characteristic not 2, and let \(R\) be a Hasse domain of \(F\) with odd class number \(h_R\). The author proves that if \(V\) is a regular quadratic \(F\)-space of dimension \(\geq 5\) and \(L\) is an \(R\)-lattice on \(V\), then \(L\) has an orthogonal splitting \(L=L_1\perp L_2\perp \cdots \perp L_t\) in which rank \(L_i=2\), for \(1\leq i\leq t-1\), and rank \(L_t\leq 4\). It improves his earlier result [Am. J. Math. 91, 106--134 (1969; Zbl 0179.08001)] which was proved under the assumption \(h_R=1\).
scientific article; zbMATH DE number 4061322