Vol. 15, No. 1, 2021

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

Tariq Syed

Vol. 15 (2021), No. 1, 109–140
Abstract

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

Keywords
cancellation, projective module, stably free module, Vaserstein symbol
Mathematical Subject Classification 2010
Primary: 19A13
Secondary: 13C10, 14F42, 19G38
Milestones
Received: 16 July 2019
Revised: 3 June 2020
Accepted: 2 July 2020
Published: 1 March 2021
Authors
Tariq Syed
Fakultät für Mathematik
Universität Duisburg-Essen
Essen
Germany