4 papers
Hyperbolicity over function fields of quadrics
James O'Shea
A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolici…
Group and round quadratic forms
James O'Shea
We offer some elementary characterisations of group and round quadratic forms. These characterisations are applied to establish new (and recover existing) characterisations of Pfis…
Multiples of Pfister forms
James O'Shea
The isotropy of multiples of Pfister forms is studied. In particular, an improved lower bound on the values of their first Witt indices is obtained. A number of corollaries of this…
Isotropy of multiples of Pfister forms and weak isotropy of forms over field extensions
James O'Shea
The isotropy of multiples of Pfister forms is studied. In particular, an improved lower bound on the value of their first Witt index is obtained. This result and certain of its cor…