函数域上二次形式各向同性的局部-全局原理失效

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2024-09-18 DOI:10.2140/ant.2024.18.1497

Asher Auel, V. Suresh

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引用次数: 0

摘要

我们证明了在特征≠2 的代数闭域上超越度 n≥2 的函数域中，2n 变量二次型的各向同性在离散估值方面的局部-全局原理的失效。我们的构造涉及博尔察和辛克与胡莱克所考虑的广义库默尔变项，以及关于离散值域上椭圆曲线乘积的非ramified同调的新结果。

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

We prove the failure of the local-global principle, with respect to discrete valuations, for isotropy of quadratic forms in $2^{n}$ variables over function fields of transcendence degree $n \geq 2$ over an algebraically closed field of characteristic $\neq 2$ . Our construction involves the generalized Kummer varieties considered by Borcea and by Cynk and Hulek as well as new results on the nontriviality of unramified cohomology of products of elliptic curves over discretely valued fields.

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.