A Criterion for Splitting of a Projective Module in Terms of Its Generic Sections.

Let |$R$| be a smooth affine domain of dimension |$d\geq 3$| over |$\overline{{\mathbb{F}}}_p$| with |$p\neq 2$|⁠. Let |$P$| be a projective |$R$| -module of rank |$d-1$| with trivial determinant. We prove that |$P$| splits off a free summand of rank 1 if and only if |$P$| surjects onto a complete intersection ideal of height |$d-1$|⁠. [ABSTRACT FROM AUTHOR]