论文标题
二次形式的稳定异性等效性的一些标准
Some criteria for stably birational equivalence of quadratic forms
论文作者
论文摘要
令$φ$和$ψ$是二次形式的特征$ k $不同于2的字段$ k $。在本文中，我们在表示形式的$ψ$的功能字段上给出了$φ$的标准，并且我们将其应用于稳定的$φ$ $ $ $ $和$ψ$的稳定的birational等价。然后，我们使用此标准来研究Pfister形式倍数的稳定生育等效的情况。最后，我们从旋转型规范的内核中给出了二次形式的稳定的二次形式的标准。
Let $φ$ and $ψ$ be quadratic forms over a field $K$ of characteristic different from 2. In this paper, we give a criterion for isotropy of $φ$ over the function field of $ψ$ in terms of representations and we apply it to stably birational equivalence of $φ$ and $ψ$. Then we use this criterion to investigate the case of stably birational equivalence of multiples of Pfister forms. Finally, we give a a criterion of stably birational equivalence of quadratic forms in terms of isomorphisms of quotients of special Clifford groups by the kernel of the spinor norm.
