Isotropy of quadratic forms over function fields in characteristic 2

Abstract

We extend to characteristic two recent results about isotropy of quadratic forms over function fields. In particular, we provide a characterization of function fields not only of quadratic forms but also more generally of polynomials in several variables, over which a quadratic form becomes isotropic. As an application of these results, we obtain criteria for stable birational equivalence of quadratic forms.

Keywords:

• Isotropic
• nondefective quadratic forms
• quadratic forms

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 11E04
• 11E81
• 14E99

Disclosure Statement

The author reports there are no competing interests to declare.

Additional information

Funding

This work was supported by DFG project HO 4784/2-1. The author further acknowledges support from the Pacific Institute for the Mathematical Sciences and a partial support from the National Science and Engineering Research Council of Canada. The research and findings may not reflect those of these institutions.