Anisotropy of quadratic forms over global fields of characteristic $\ne$ 2 is diophantine

Abstract

We prove that the set of anisotropic quadratic forms over global fields of characteristic different from 2 is a diophantine set. Our proof builds upon and extends the method of Koenigsmann, using tools from class field theory, the local-global principle, and advances on the diophantine definability of non-norm sets over global fields.