Methods in complete intersections in corank one

Abstract

Let $A$ denote an affine algebra over an algebraically closed field $\mathbb{F}$, with $\dim A=d\ge 3$. Due to the recent exciting activities regarding projective $A$-modules $P$, with $rankP=d-1$ (corank one), we explore the corank zero methods of N. Mohan Kumar and M. P. Murthy, in the complete intersections theory. We hypothesize regarding cancellation properties projective modules of corank one, and derive some of analogues of the results in corank zero case. We obtain some affirmative results, when $A$ is an affine algebra over ${\overline{\mathbb{F}}}_p$.

Added some affirmation results, in the positive characteristic case