Projective modules over affine threefolds: a simpler case

Abstract

Let $p\ne 2$, and let $R$ be a smooth affine algebra of dimension $3$ over ${\overline{F}}_p$ and $P,Q$ be projective $R$-modules of rank $2$, each with trivial determinant. We prove: $P$ is isomorphic to $Q$ if and only if there is an ideal $J\subset R$ of height $2$ such that both $P$ and $Q$ map onto $J$.

This one will be merged with the revised version of "On two conjectures of Murthy" (arXiv:1710.04281)