We prove that a quadratic A[T]-module Q with Witt index (Q/TQ)≥d, where d is the dimension of the equicharacteristic regular local ring A, is extended from A. This improves a theorem of the second named author who showed it when A is the local ring at a smooth point of an affine variety over an infinite field. To establish our result, we need to establish a local-global principle (of Quillen) for the Dickson- Siegel-Eichler-Roy (DSER) elementary orthogonal transformations.
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