Isotropy of quadratic forms over function fields in characteristic 2

TL;DR

This paper extends recent results on when quadratic forms become isotropic over function fields in characteristic two, providing new criteria for stable birational equivalence and broadening understanding of quadratic forms and polynomials.

Contribution

It offers a characterization of function fields where quadratic forms and polynomials become isotropic in characteristic two, and applies these to criteria for stable birational equivalence.

Findings

Characterization of function fields where quadratic forms are isotropic in characteristic two

Criteria for stable birational equivalence of quadratic forms

Extension of recent isotropy results to more general polynomials

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.