Anisotropy of quadratic forms over global fields of characteristic $\ne$ 2 is diophantine
Volume 225 / 2026
Acta Arithmetica 225 (2026), 101-125
MSC: Primary 11U05; Secondary 11R37
DOI: 10.4064/aa240724-7-9
Published online: 13 October 2026
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 nonnorm sets over global fields.
