Hasse principles for quadratic forms over function fields
Hasse principles for quadratic forms over function fields
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DOI：
10.1016/j.jalgebra.2023.04.007
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发表时间：
2022-04
影响因子：
0.9
通讯作者：
Connor Cassady
中科院分区：
文献类型：
--
作者：
Connor Cassady
我们研究了二次型在不同离散赋值集上的各向同性和等距性的哈塞原理。在满足性质A i（2）的域的纯超越域扩张上，我们发现了许多关于相对较小的离散赋值集的各向同性哈塞原理的反例。对于特征为λ 2的代数闭域上超越度为r的广义生成域扩张K，我们利用Auel和Suresh关于各向同性的Hasse原理的2 r维反例，得到了关于函数域K的簇所诱导的整除离散赋值的低维反例.
We investigate the Hasse principles for isotropy and isometry of quadratic forms over finitely generated field extensions with respect to various sets of discrete valuations. Over purely transcendental field extensions of fields that satisfy property A i (2) for some i, we find numerous counterexamples to the Hasse principle for isotropy with respect to a relatively small set of discrete valuations. For finitely generated field extensions K of transcendence degree r over an algebraically closed field of characteristic≠ 2, we use the 2 r-dimensional counterexample to the Hasse principle for isotropy due to Auel and Suresh to obtain counterexamples of lower dimensions with respect to the divisorial discrete valuations induced by a variety with function field K.