12次和8次正交对合的Araason不变量及Brauer群的四元子群
The Arason invariant of orthogonal involutions of degree 12 and 8, and quaternionic subgroups of the Brauer group
摘要：
使用Rost不变量的torsors下自旋群可以定义一个类似的Araason不变量的某些埃尔米特形式和正交对合。我们计算这个不变量明确在各种情况下，并使用它来关联到每一个正交对合平凡的判别式和平凡的Clifford不变量的中心单代数，甚至共同指数的上同调类$f_3$的程度为3与$μ_2$系数。这个不变量$f_3$是任何阿拉森不变量的两倍;当代数的次数至多为10时，它消失，并且当中心有一个二次扩张，同时分裂代数并使对合成为双曲时。本文提供了一个详细的研究这两个不变量，特别注意度12的情况下，并与存在的二次分裂字段的关系。
英文摘要：
Using the Rost invariant for torsors under Spin groups one may define an analogue of the Arason invariant for certain hermitian forms and orthogonal involutions. We calculate this invariant explicitly in various cases, and use it to associate to every orthogonal involution with trivial discriminant and trivial Clifford invariant over a central simple algebra of even co-index a cohomology class $f_3$ of degree 3 with $μ_2$ coefficients. This invariant $f_3$ is the double of any representative of the Arason invariant; it vanishes when the algebra has degree at most 10, and also when there is a quadratic extension of the center that simultaneously splits the algebra and makes the involution hyperbolic. The paper provides a detailed study of both invariants, with particular attention to the degree 12 case, and to the relation with the existence of a quadratic splitting field.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
