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

2014/01/04 by A. A. Ambily, Ambily, A. A., Ravi A. Rao +1 · 1 citation
Mathematics · #Mathematical Dynamics and Fractals #Algebraic Geometry and Number Theory #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1401.0809

Abstract

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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• Horrocks theorem for odd orthogonal groups

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