We prove that a quadratic $A[T]$-module $Q$ with Witt index ($Q/TQ$)$ \geqd$, where $d$ is the dimension of the equicharacteristic regular local ring$A$, is extended from $A$. This improves a theorem of the second named authorwho showed it when $A$ is the local ring at a smooth point of an affine varietyover an infinite field. To establish our result, we need to establish aLocal-Global Principle (of Quillen) for the Dickson--Siegel--Eichler--Roy(DSER) elementary orthogonal transformations.
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机译：我们证明具有Witt指数（$ Q / TQ $）$ \ geqd $的二次$ A [T] $-模块$ Q $被扩展，其中$ d $是等特征的常规局部环$ A $的尺寸从$ A $。这改进了第二个定理的定理，该定理在$ A $是无限范围内仿射变体的平滑点处的局部环时显示。为了确定结果，我们需要为Dickson-Siegel-Eichler-Roy（DSER）基本正交变换建立（Quillen）局部局部原则。
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