Extendability of quadratic modules over a polynomial extension of an equicharacteristic regular local ring

Abstract

We prove that a quadratic $A[T]$-module $Q$ with Witt index ($Q/TQ$)$\ge d$, 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.

19 pages

References in corpus (1)

• Yoga of Commutators in Roy's Elementary Orthogonal Group

Cited by in corpus (2)

• Yoga of Commutators in Roy's Elementary Orthogonal Group
• Normality and $K_1$-stability of Roy's elementary orthogonal group