Title: Witt invariants of quaternionic forms Show Chinese title

Title: 四元数型的Witt不变量

Abstract: We describe all Witt invariants of anti-hermitian forms over a quaternion algebra with its canonical involution, and in particular all Witt invariants of orthogonal groups $O(A,\sigma)$ where $(A,\sigma)$ is an central simple algebra with orthogonal involution and $A$ has index $2$. They are combinations of appropriately defined $\lambda$-powers, similarly to the case of quadratic forms, but the module of invariants is no longer free over those operations. The method involves extending the scalars to a generic splitting field of $A$, and controlling the residues of the invariants with respect to valuations coming from closed points in the Severi-Brauer variety. Show Chinese abstract

Abstract: 我们描述了四元数代数上关于典范对合的反 Hermite 形式的所有 Witt 不变量，并且特别地描述了正交群 $O(A,\sigma)$ 的所有 Witt 不变量，其中 $(A,\sigma)$ 是具有正交对合的中心单代数，而 $A$ 的指标为 $2$。 它们是由适当定义的 $\lambda$-幂组合而成的，类似于二次型的情况，但不变量模不再自由生成于这些运算之上。 该方法涉及将标量扩展到 $A$ 的通用分裂域，并通过控制来自 Severi-Brauer 品种闭点的赋值所对应的不变量残差来完成分析。