域扩张上Pfister型的重式的迷向性和型的弱迷向性
Isotropy of multiples of Pfister forms and weak isotropy of forms over field extensions
摘要：
研究了Pfister型的倍数的各向同性。特别地，得到了它们的第一Witt指数的一个改进的下界.这个结果及其某些推论被应用于任意二次型的弱迷向指数（或等价地，子级）的研究。这个不变量和水平的（二次）形式之间的关系进行了研究。讨论了确定形式关于域扩张的弱各向同性指数的值集的问题，确定了允许整数和不允许整数。类似的调查方面的一个形式的水平也进行了，与一些问题提出的Berhuy，Grenier-Boley和Mahmoudi正在解决。弱各向同性指数和水平的圆形和Pfister形式的检查结束本文。
英文摘要：
The isotropy of multiples of Pfister forms is studied. In particular, an improved lower bound on the value of their first Witt index is obtained. This result and certain of its corollaries are applied to the study of the weak isotropy index (or equivalently, the sublevel) of arbitrary quadratic forms. The relationship between this invariant and the level of the (quadratic) form is investigated. The problem of determining the set of values of the weak isotropy index of a form with respect to field extensions is addressed, with both admissible and inadmissible integers being determined. The analogous investigation with respect to the level of a form is also undertaken, with some questions asked by Berhuy, Grenier-Boley and Mahmoudi being resolved. An examination of the weak isotropy index and the level of round and Pfister forms concludes this article.
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