Some criteria for stably birational equivalence of quadratic forms

Abstract

Let $\phi$ and $\psi$ be quadratic forms over a field $K$ of characteristic different from 2. In this paper, we give a criterion for isotropy of $\phi$ over the function field of $\psi$ in terms of representations and we apply it to stably birational equivalence of $\phi$ and $\psi$. Then we use this criterion to investigate the case of stably birational equivalence of multiples of Pfister forms. Finally, we give a a criterion of stably birational equivalence of quadratic forms in terms of isomorphisms of quotients of special Clifford groups by the kernel of the spinor norm.

16 pages

Cited by in corpus (1)

• Isotropy of quadratic forms over function fields in characteristic 2