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arXiv · 1709.03707

Failure of the local-global principle for isotropy of quadratic forms over function fields

Asher Auel·V. Suresh
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Abstract

We prove the failure of the local-global principle, with respect to discrete valuations, for isotropy of quadratic forms over function fields of transcendence degree at least 2 over algebraically closed fields. Our construction involves generalized Kummer varieties as well as a new nontriviality result for the unramified cohomology of products of elliptic curves over discretely valued fields, which can be viewed as an arithmetic version of a theorem of Gabber.

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Asher Auel, V. Suresh. 2023-10-20. Failure of the local-global principle for isotropy of quadratic forms over function fields. https://doi.org/10.2140/ant.2024.18.1497

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