论文标题
方形反射多项式
Square-reflexive polynomials
论文作者
论文摘要
对于特征的字段$ e $不同于$ 2 $和共同学$ 2 $ - 数字一号，研究了合理功能字段$ e（x）$的二次形式。在$ e [x] $中，以$ e（x）$超过$ e（x）$在$ e [x] $中的多项式方面的表征满足了本地全球全球原则，这些原则对于$ e $的离散估值。这样，在$ e $有限的或伪代数关闭的情况下，可以实现针对本地全球原则的新基本证明。这项研究得到了各种例子的补充。
For a field $E$ of characteristic different from $2$ and cohomological $2$-dimension one, quadratic forms over the rational function field $E(X)$ are studied. A characterisation in terms of polynomials in $E[X]$ is obtained for having that quadratic forms over $E(X)$ satisfy a local-global principle with respect to discrete valuations that are trivial on $E$. In this way new elementary proofs for the local-global principle are achieved in the cases where $E$ is finite or pseudo-algebraically closed. The study is complemented by various examples.
