Cancellation of vector bundles of rank 3 with trivial Chern classes on smooth affine fourfolds

نویسندگان

چکیده

If n≡0,1mod4, we prove a sum formula Vθ0(a0,aRn)=n⋅Vθ0(a0,aR) for the generalized Vaserstein symbol whenever R is smooth affine algebra over perfect field k with char(k)≠2 such that −1∈k×2. This enables us to generalize result of Fasel-Rao-Swan on transformations unimodular rows via elementary matrices normal algebras dimension d≥4 algebraically closed fields characteristic ≠2. As consequence, any projective module rank 3 trivial Chern classes 4 an char(k)≠2,3 cancellative.

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ژورنال

عنوان ژورنال: Journal of Pure and Applied Algebra

سال: 2022

ISSN: ['1873-1376', '0022-4049']

DOI: https://doi.org/10.1016/j.jpaa.2022.107038