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arXiv · 1711.08210

A generalized Vaserstein symbol

Tariq Syed
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Abstract

Let $R$ be a commutative ring. For any projective $R$-module $P_0$ of constant rank $2$ with a trivialization of its determinant, we define a generalized Vaserstein symbol on the orbit space of the set of epimorphisms $P_0 \oplus R \rightarrow R$ under the action of the group of elementary automorphisms of $P_0 \oplus R$, 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 $R$ is a regular Noetherian ring of dimension $2$ or a regular affine algebra of dimension $3$ over a perfect field $k$ with $c.d.(k) \leq 1$ and $6 \in k^{\times}$.

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Tariq Syed. 2020-02-21. A generalized Vaserstein symbol. https://doi.org/10.2140/akt.2019.4.671

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