论文标题
部分可观测时空混沌系统的无模型预测
Hasse principles for quadratic forms over function fields
论文作者
论文摘要
我们研究了相对于各种离散估值集，研究二次形式的各向同性和等轴测图的HASSE原理。对于某些$ i $，在满足属性$ \ mathscr {a} _i（2）$的字段的纯粹先验场扩展中，我们在相对较小的离散估值方面找到了许多同性恋原理的反示例。对于有限生成的现场扩展，超越$ r $ $ r $在代数封闭的特征性$ \ ne 2 $上，我们使用$ 2^r $ $ - 维度的反例来对同位素的hasse原理，因为Auel和Suresh的Suresh和Suresh的较低尺寸相对于ivalive contive的较低尺寸，以划分为iDrive coptive undive的$ k $。
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 $\mathscr{A}_i(2)$ 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 $\ne 2$, 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 $K$.
