Cancellation of projective modules in polynomial rings of prime characteristic

Sourjya Banerjee

paper

Cancellation of projective modules in polynomial rings of prime characteristic

arXiv:2210.17337

Abstract

Let $A$ be a commutative Noetherian ring of characteristic $p > 0$ , such that $dim (A) = d$ . Let $P$ be a projective $A [T_{1}, ..., T_{n}]$ -module of rank $d$ . We show that $P$ is cancellative if and only if $P / < T_{1}, ..., T_{n} > P$ is cancellative. We deduce some applications. In one of the interesting consequences, we show that the Bass-Quillen conjecture has an affirmative answer in dimension three, when $2$ is invertible.

arXiv commentThe proof of 2.2 is not correct