Failure of the local-global principle for isotropy of quadratic forms over function fields
Algebraic Geometry
2024-09-18 v3 Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1709.03707,
title = {Failure of the local-global principle for isotropy of quadratic forms over function fields},
author = {Asher Auel and V. Suresh},
journal= {arXiv preprint arXiv:1709.03707},
year = {2024}
}
Comments
15 pages, final version accepted in Algebra & Number Theory