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Abstract
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Let
be a commutative ring.
For any projective
-module
of constant
rank
with a trivialization of its determinant, we define a generalized
Vaserstein symbol on the orbit space of the set of epimorphisms
under the action of the group of elementary automorphisms of
, which
maps into the elementary symplectic Witt group. We give criteria for the surjectivity and
injectivity of the generalized Vaserstein symbol and deduce that it is an isomorphism if
is a regular Noetherian ring
of dimension
or a regular
affine algebra of dimension
over a perfect field
with
and
.
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Keywords
generalized Vaserstein symbol
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Mathematical Subject Classification 2010
Primary: 13C10, 14F42, 19A13, 19G38
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Milestones
Received: 13 April 2018
Revised: 17 April 2019
Accepted: 2 May 2019
Published: 10 January 2020
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