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arXiv · 2401.00537

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

Guang Hu
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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.

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Guang Hu. 2023-12-31. Anisotropy of quadratic forms over global fields of characteristic $\neq$ 2 is diophantine. https://arxiv.org/abs/2401.00537

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