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arXiv · 1902.01130

The cancellation of projective modules of rank 2 with a trivial determinant

Tariq Syed
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Abstract

We study the cancellation property of projective modules of rank $2$ with a trivial determinant over Noetherian rings of dimension $\leq 4$. If $R$ is a smooth affine algebra of dimension $4$ over an algebraically closed field $k$ such that $6 \in k^{\times}$, then we prove that stably free $R$-modules of rank $2$ are free if and only if a Hermitian $K$-theory group $\tilde{V}_{SL} (R)$ is trivial.

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Tariq Syed. 2019-02-04. The cancellation of projective modules of rank 2 with a trivial determinant. https://doi.org/10.2140/ant.2021.15.109

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