On a conjecture of Murthy

This article concerns Murthy's conjecture on complete intersections, made in 1975. The sole breakthrough on this conjecture has still been the result proved by Mohan Kumar in 1978. The conjecture is open in general. In this article we improve Mohan Kumar's bound when the base field is F‾p. As an application, we prove that any local complete intersection surface in the affine space AF‾pd is a set-theoretic complete intersection, generalizing a result of Bloch-Murthy-Szpiro.