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arXiv · 1401.0809

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

A. A. Ambily·Ravi A. Rao
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Abstract

We prove that a quadratic $A[T]$-module $Q$ with Witt index ($Q/TQ$)$ \geq 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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A. A. Ambily, Ravi A. Rao. 2014-01-04. Extendability of quadratic modules over a polynomial extension of an equicharacteristic regular local ring. https://arxiv.org/abs/1401.0809

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