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Extendability of quadratic modules over a polynomial extension of an equicharacteristic regular local ring
We prove that a quadratic -module with Witt index (), where is the dimension of the equicharacteristic regular local ring
, is extended from . This improves a theorem of the second named author
who showed it when 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.Comment: 19 page
Quillen-Suslin theory for a structure theorem for the Elementary Symplectic Group
A new set of elementary symplectic elements is described, It is shown that
these also generate the elementary symplectic group {\rm ESp}. These
generators are more symmetrical than the usual ones, and are useful to study
the action of the elementary symplectic group on unimodular rows. Also, an
alternate proof of, {\rm ESp} is a normal subgroup of {\rm
Sp}, is shown using the Local Global Principle of D. Quillen for the
new set of generators.Comment: 14 pages, few typos corrected. To appear in Ramanujan Math. Soc.
Lect. Notes Se
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