Failure of the local-global principle for isotropy of quadratic forms over function fields
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866913504010698752 |
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| author | Auel, Asher Suresh, V. |
| author_facet | Auel, Asher Suresh, V. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1709_03707 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Failure of the local-global principle for isotropy of quadratic forms over function fields Auel, Asher Suresh, V. Algebraic Geometry Rings and Algebras 11E81, 11R58, 12G05, 14C25, 14F22, 14G12, 14H52, 14J20, 14J28, 14J32, 16W60, 19D45 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. |
| title | Failure of the local-global principle for isotropy of quadratic forms over function fields |
| topic | Algebraic Geometry Rings and Algebras 11E81, 11R58, 12G05, 14C25, 14F22, 14G12, 14H52, 14J20, 14J28, 14J32, 16W60, 19D45 |
| url | https://arxiv.org/abs/1709.03707 |