论文标题
Pfister的Azumaya代数的本地全球原则
Pfister's local-global principle for Azumaya algebras with involution
论文作者
论文摘要
我们证明了Pfister在Azumaya代数上的Hermitian形式的局部全球原则，而半落地圈则尤其表明，非词性Hermitian形式的Witt Group是$ 2 $ 2 $ - 主要的扭转。我们的证明依赖于希尔维斯特的惯性定律的隐居版本，该定律是从对Garrel广泛研究的Hermitian形式配对之间的联系，Hermitian形式的签名和积极的半芬太尼二次形式进行的。
We prove Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular hermitian forms is $2$-primary torsion. Our proof relies on a hermitian version of Sylvester's law of inertia, which is obtained from an investigation of the connections between a pairing of hermitian forms extensively studied by Garrel, signatures of hermitian forms, and positive semidefinite quadratic forms.
